Tesi sul tema "Serial property"

The focus of the present study is on managerial organization employed for serial properties registered on the UNESCO World Heritage List. The research examines a specific type of cultural heritage, precisely the sites, which combine architecture and landscape design, such as princely estates, palace and park ensembles or villas. Widely spread in Europe, they reflect upon historical past of the countries, evoking ideas of a nation state and identity. The research examines former Imperial residences turned museums located in the suburbs of St. Petersburg. Six palace and park ensembles are included into the UNESCO World Heritage Site (WHS): ‘Historic Center of St. Petersburg and related groups of monuments’ [WHS №540bis]. On one hand, these estates are uniformly perceived as a whole, due to their association with the Russian Imperial family, their uniform inscription as a serial property within a single UNESCO world heritage site and a brand of ‘the Golden/Emerald/Green Necklace/Ring of St. Petersburg’. On the other hand, disproportionate differences in administration, territorial subordination, state of conservation, services and offers, promotion and visibility demonstrate the residence museums to be separate parts of a disintegrated system. Consequently, the research aims to analyse the model of St. Petersburg suburban residence museums’ in its functioning, taking into consideration multiple aspects, such as legal status, administration, management, visitors, services, etc. Accordingly, to provide a comprehensive study of the St. Petersburg model and to examine some of its components in depth, an extensive analysis of relevant European practices is implemented. The examples selected in Germany and Italy comprise: Palaces and Parks of Potsdam and Berlin [WHS N. 532ter, 1990], Residences of Ludwig II in Bavaria (nomination resubmitted); The Residences of the Royal House of Savoy [WHS N.23bis, 1997], Medici Villas and Gardens in Tuscany [WHS N.175, 2013].

Ce travail de recherche entend analyser les évolutions du processus de patrimonialisation dans le temps et dans l'espace. Il entreprend ainsi d'étudier les transformations et les reproductions urbaines du centre historique de Bologne depuis la période d'unification du nouvel État italien jusqu'à l'inscription des portiques de la ville au Patrimoine mondial de l'Unesco. Il part pour cela du renouvellement des représentations et des pratiques des habitants, et de la parallèle institutionnalisation du patrimoine urbain à différentes échelles.L'histoire de cet espace urbain et de ses progressives intégrations vers un territoire communal élargi atteste de la diversification des biens culturels sur la période concernée, depuis les monuments nationaux jusqu'au patrimoine diffus qui fonde la typicité des lieux. Elle révèle un système patrimonial composé d'éléments architecturaux et urbanistiques interconnectés et polarisés. Cette composition résulte de la stratification et de l'articulation des patrimonialisations dont le centre historique représente l'archétype.Suivant une démarche géohistorique, cette thèse entend comparer dans le temps et dans l'espace les rapports des acteurs à leurs biens culturels. L'enjeu est à la fois d'approfondir la compréhension de la complexification constatée du patrimoine, mais aussi de questionner les patrimonialisations comme des dynamiques socio-spatiales qui interagissent avec l'aménagement et la gestion du territoire
The aim of this research project is to analyse the evolution of the heritage development process in time and space. It sets out to study the transformations and urban reproductions of the historic centre of Bologna from the period of the unification of the new Italian state to the inclusion of the city's porticoes on UNESCO's World Heritage List. It takes as its starting point the renewed representations and practices of the city's inhabitants, and the parallel institutionalisation of urban heritage at different scales.The history of this urban area and its gradual integration into a wider municipal territory demonstrates the diversification of cultural properties over the period in question, from national monuments to the diffuse heritage that forms the basis of local typicality. It reveals a heritage system made up of interconnected and polarised architectural and town-planning elements. This composition is the result of the stratification and articulation of heritage developments, of which the historic centre is the archetype.Following a geohistorical approach, this thesis sets out to compare, in time and space, the relationships between actors and their cultural properties. The aim is not only to gain a deeper understanding of the increasing complexity of heritage, but also to examine heritage development as a socio-spatial dynamic that interacts with spatial planning and territory management

Thesis (Ph. D.)--University of California, San Diego, 2009.
Title from first page of PDF file (viewed September 17, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 234-241).

Constructive reverse mathematics is a programme in which non- and semi-constructive principles are classified in accordance with which other principles they imply or are implied by, relative to the framework of Bishop-style constructive mathematics. One such principle that has come under focus in recent years is an antithesis of Specker's theorem (that theorem being a characteristic result of Russian recursive mathematics): this so-called anti-Specker property is intuitionistically valid, and of considerable utility in proving results of real and complex analysis. We introduce several new weakenings of the anti-Specker property and explore their role in constructive reverse mathematics, identifying implication relationships that they stand in to other notable principles. These include, but are not limited to: variations upon Brouwer's fan theorem, certain compactness properties, and so-called zero-stability properties. We also give similar classification results for principles arising directly from Specker's theorem itself, and present new, direct proofs of related fan-theoretic results. We investigate how anti-Specker properties, alongside power-series-based arguments, enable us to recover information about the structure of holomorphic functions: in particular, they allow us to streamline a sequence of maximum-modulus theorems.

Uloga kulture u društvenim promenama javlja se kao nezaobilazna tema u kontekstu postsocijalističketranzicije. Ispostavilo se da institucionalna transformacija političkog i ekonomskog uređenja društva nijedovoljna, te da uspeh institucionalnih promena uveliko zavisi od nacionalne kulture, i promena na nivou celenacije (Elste, Offe, Preuss, 1998:19). Ekonomska strana tranzicije se pokazala posebno problematičnom jerekonomske aktivnosti čine veliki deo svakodnevice svakog pripadnika društva, neprestano ukazujući naprobleme vezane za ekonomsku transformaciju društva. Kada se od nje odvoje apstraktni pokazatelji kojimase savremeni ekonomisti služe očito je da ekonomija sama jeste deo kulture (Beugelsdijk i Maseland,2014:116). Društvene i kulturne promene u osnovnoj strukturi i vrsti modifikacija kulturnih institucija tokomnekog vremenskog perioda ogledaju se kroz kulturne obrasce (Koković 2005: 228). Primenjujući savremeneekonomske metode i teorije novi institucionalni ekonomisti uglavnom pokušavaju da izbegnu argumentacijuprisutnu u drugim društvenim naukama – argumentaciju da institucije nisu rezultat efikasnog rešenjaekonomskih problema (Granovetter u Biggard ed. 2002:88), već nešto mnogo kompleksnije. Ipak, kako sekulturni obrasci manifestuju kao ustaljeni načini ponašanja te stoga predstavljaju relativno stabilne pojave,oni su takođe i temelj institucionalizacije – kada se takva ponašanja nađu u okviru većih koherentnih celinaprerastaju u institucionalizovano ponašanje, učestvujući u izgradnji institucije (Koković 2005: 228). Jedan odnedovoljno istraženih pristupa u sociologiji kulture je legitimacija kulturnih obrazaca, i sledstveno tomelegitimacija institucija i institucionalnih sistema. Mehanizmi legitimacije kao socijalne činjenice zahvataju uširoko polje kulture, uključujući socijalnu strukturu, odnose moći i slično, pa se ne mogu posmatrati mimotoga (Berger, Luckmann, 1991. Searl, 1996). Sa svoja četri funkcionalna nivoa, prema Bergeru i Lukmanu,legitimacija povezuje čitav socio-kulturni svet zajednice i pripadajućih individua. U kontekstupostsocijalističke tranzicije u Srbiji stanje ekonomske kulture se posebno manifestuje na relacijama izmeđuinstitucija svojine, tržišta i nacionalne države, kao specifičnih artikulacija srpske kulture, i za njih vezanekulturne obrasce.Disertacija je imala za cilj da pruži uvid u odnos između institucija svojine, tržišta i države kao jednoginstitucionalnog sklopa iz perspektive ekonomske kulture, a oslanjajući se prvenstveno na legitimacijuinstitucionalnih i kulturnih obrazaca i sistema. Imajući u vidu složenost zadatka – stanje u savremenomsrpskom društvu trebalo je objasniti i iz istorijske perspektive – bilo je neophodno kombinovati različitu vrstugrađe i evidencije, i u skladu sa tim različite metode opisa, analize i interpretacije. Pored istorijske građe iradova autora koji su istraživali socioekonomske aspekte srpskog društva i istorije korišćena je empirijskeevidencija prikupljena u okviru Evropskog istraživanja vrednosti (EVS) i Projekta jugoistočnog socijalnogistraživanja (SEESSP). Pomenuta empirijska građa obrađna je klaster analizom kako bi se utvrdililegitimacijski obrasci koji korespondiraju kulturnim obrascima u savremnom srpskom društvu. Korišćenjemistorijske i savremene evidencije trebalo je utvrditi kakvu ulogu u srpskoj ekonomskoj kulturi ima institucijatržišta, i u kakvom je odnosu sa institucijama svojine i države, kao i kako se to menjalo kroz razvoj srpskedržave od XIX veka naovamo – kako se u ovom kulturno-institucionalnom trouglu organizovao ekonomskiživot srpskog društva.U teorijsko-metodološkom pogledu pokazalo se da su legitimacijski mehanizmi solidni pokazatelji kulturnihobrazaca čak i kada korišćeni podaci nisu optimalni. Sa druge strane, a nimalo neočekivano, ispostavilo se dauvođenje tržišnih mehanizama u ekonomiju društva kontekstualno uslovljen postojećim institucionalnimograničenjima vezanim za svojinu i državno uređenje, kao i šire kulturne obrasce i etičke norme društva. Nemože se govoriti o uvođenju ili neuvođenju tržišne ekonomije, već o spcefičnim tržišnim mehanizmima injihovoj strukturi i poziciji u ukupnoj ekonomskoj aktivnosti i kulturi društva.Kada je reč o srpskom društvu, identifikovani kulturni obrasci potvrđuju nalaze drugih autora o kulturi ukojoj značajno mesto zauzimaju egalitaristički principi, kolektivizam, i oslanjanje na državu kaodominantnog ekonomskog arbitra. Istorijska analiza takođe sugeriše da takva kultura nije rezultatvišedecenijskog socijalizma, već joj koreni sežu mnogo dalje u prošlost, pojavljujući se kao karakteristikazajednička različitim socio-političkim uređenjima. Kulturni obrasci iz prve decenije XXI veka ukazuju dapostoji legitimacijski deficit kad je u pitanju tržište. Tržište u srpskoj kulturi nije institucionalizovano kaomehanizam pogodan za distribuciju bogatstva, odnosno, većina kulturnih obrazaca ne pozicionira tržište kaodobar kriterijum regulacije materijalnih nejednakosti. Takođe, iako većinu kulturnih obrazaca karakterišepreferencija privatne svojine, uočljiva su opredeljenja uspostavljena etičkim normama koje važe u srpskom Uloga kulture u društvenim promenama javlja se kao nezaobilazna tema u kontekstu postsocijalističketranzicije. Ispostavilo se da institucionalna transformacija političkog i ekonomskog uređenja društva nijedovoljna, te da uspeh institucionalnih promena uveliko zavisi od nacionalne kulture, i promena na nivou celenacije (Elste, Offe, Preuss, 1998:19). Ekonomska strana tranzicije se pokazala posebno problematičnom jerekonomske aktivnosti čine veliki deo svakodnevice svakog pripadnika društva, neprestano ukazujući naprobleme vezane za ekonomsku transformaciju društva. Kada se od nje odvoje apstraktni pokazatelji kojimase savremeni ekonomisti služe očito je da ekonomija sama jeste deo kulture (Beugelsdijk i Maseland,2014:116). Društvene i kulturne promene u osnovnoj strukturi i vrsti modifikacija kulturnih institucija tokomnekog vremenskog perioda ogledaju se kroz kulturne obrasce (Koković 2005: 228). Primenjujući savremeneekonomske metode i teorije novi institucionalni ekonomisti uglavnom pokušavaju da izbegnu argumentacijuprisutnu u drugim društvenim naukama – argumentaciju da institucije nisu rezultat efikasnog rešenjaekonomskih problema (Granovetter u Biggard ed. 2002:88), već nešto mnogo kompleksnije. Ipak, kako sekulturni obrasci manifestuju kao ustaljeni načini ponašanja te stoga predstavljaju relativno stabilne pojave,oni su takođe i temelj institucionalizacije – kada se takva ponašanja nađu u okviru većih koherentnih celinaprerastaju u institucionalizovano ponašanje, učestvujući u izgradnji institucije (Koković 2005: 228). Jedan odnedovoljno istraženih pristupa u sociologiji kulture je legitimacija kulturnih obrazaca, i sledstveno tomelegitimacija institucija i institucionalnih sistema. Mehanizmi legitimacije kao socijalne činjenice zahvataju uširoko polje kulture, uključujući socijalnu strukturu, odnose moći i slično, pa se ne mogu posmatrati mimotoga (Berger, Luckmann, 1991. Searl, 1996). Sa svoja četri funkcionalna nivoa, prema Bergeru i Lukmanu,legitimacija povezuje čitav socio-kulturni svet zajednice i pripadajućih individua. U kontekstupostsocijalističke tranzicije u Srbiji stanje ekonomske kulture se posebno manifestuje na relacijama izmeđuinstitucija svojine, tržišta i nacionalne države, kao specifičnih artikulacija srpske kulture, i za njih vezanekulturne obrasce.Disertacija je imala za cilj da pruži uvid u odnos između institucija svojine, tržišta i države kao jednoginstitucionalnog sklopa iz perspektive ekonomske kulture, a oslanjajući se prvenstveno na legitimacijuinstitucionalnih i kulturnih obrazaca i sistema. Imajući u vidu složenost zadatka – stanje u savremenomsrpskom društvu trebalo je objasniti i iz istorijske perspektive – bilo je neophodno kombinovati različitu vrstugrađe i evidencije, i u skladu sa tim različite metode opisa, analize i interpretacije. Pored istorijske građe iradova autora koji su istraživali socioekonomske aspekte srpskog društva i istorije korišćena je empirijskeevidencija prikupljena u okviru Evropskog istraživanja vrednosti (EVS) i Projekta jugoistočnog socijalnogistraživanja (SEESSP). Pomenuta empirijska građa obrađna je klaster analizom kako bi se utvrdililegitimacijski obrasci koji korespondiraju kulturnim obrascima u savremnom srpskom društvu. Korišćenjemistorijske i savremene evidencije trebalo je utvrditi kakvu ulogu u srpskoj ekonomskoj kulturi ima institucijatržišta, i u kakvom je odnosu sa institucijama svojine i države, kao i kako se to menjalo kroz razvoj srpskedržave od XIX veka naovamo – kako se u ovom kulturno-institucionalnom trouglu organizovao ekonomskiživot srpskog društva.U teorijsko-metodološkom pogledu pokazalo se da su legitimacijski mehanizmi solidni pokazatelji kulturnihobrazaca čak i kada korišćeni podaci nisu optimalni. Sa druge strane, a nimalo neočekivano, ispostavilo se dauvođenje tržišnih mehanizama u ekonomiju društva kontekstualno uslovljen postojećim institucionalnimograničenjima vezanim za svojinu i državno uređenje, kao i šire kulturne obrasce i etičke norme društva. Nemože se govoriti o uvođenju ili neuvođenju tržišne ekonomije, već o spcefičnim tržišnim mehanizmima injihovoj strukturi i poziciji u ukupnoj ekonomskoj aktivnosti i kulturi društva.Kada je reč o srpskom društvu, identifikovani kulturni obrasci potvrđuju nalaze drugih autora o kulturi ukojoj značajno mesto zauzimaju egalitaristički principi, kolektivizam, i oslanjanje na državu kaodominantnog ekonomskog arbitra. Istorijska analiza takođe sugeriše da takva kultura nije rezultatvišedecenijskog socijalizma, već joj koreni sežu mnogo dalje u prošlost, pojavljujući se kao karakteristikazajednička različitim socio-političkim uređenjima. Kulturni obrasci iz prve decenije XXI veka ukazuju dapostoji legitimacijski deficit kad je u pitanju tržište. Tržište u srpskoj kulturi nije institucionalizovano kaomehanizam pogodan za distribuciju bogatstva, odnosno, većina kulturnih obrazaca ne pozicionira tržište kaodobar kriterijum regulacije materijalnih nejednakosti. Takođe, iako većinu kulturnih obrazaca karakterišepreferencija privatne svojine, uočljiva su opredeljenja uspostavljena etičkim normama koje važe u srpskom.
The role of culture in social changes appears as unavoidable topic in the context of post-socialist transition. Itturned out that institutional transformation of political and economic systems is not sufficient and that socialsuccess of instituional changes depends on culture, and requires changes at the national level (Elster, Offe,Preuss, 1998:19). Economic transition has proven particularly problematic given that economic activitiesmake a significant part of daily routine for every member of a society, hence constantly bringing aboutproblems related to economic transformation of a society. Looking beyond abstract indicators contemporaryeconomists rely on economy is obviously part of culture (Beugelsdijk i Maseland, 2014:116). Social andcultural changes in structure and substance of social institutions are manifested over time as changes incultural patterns (Koković 2005: 228). By applying contemporary economic methods and theories newinstitutional economists try mainly to avoid an argument present in other social sciences – institutions are nota result of efficient solution to economic problems (Granovetter u Biggard ed. 2002:88), but rather somethingmuch more complex. Cultural patterns as habitual behavioural models manifest relatively stable phenomena,and make foundation for institutionalization – when such behaviour finds itslef within larger coherent units itturns into institutionalized behaviour, contributing to institution building (Koković 2005: 228). One of theless explored directions in sociology of culture is legitimation of cultural patterns, and subsequentlylegitimation of institutions and institutional systems. Legitimating mechanisms as identifiable social factsreach into a broad field of culture, including social structure, power relations and similar, and thereforecannot be analyzed separately (Berger, Luckmann, 1991. Searl, 1996). With four functional levels, accordingto Berger and Luckmann, legitimation connects all socio-cultural world of a community and its members. Inthe context of post-socialist transition in Serbia the state of economic culture is manifested through relationbetween institutions of property, market and national state, as specific articulations of Serbian culture andrelevant cultural patterns.The goal of the thesis was to provide insight into a relationship between institutions of property, market andthe state as an institutional entity from the perspective of economic culture, relying primarily on legitimationof institutional and cultural patterns and systems. Having in mind complexity of the task – contemporarySerbian society had to be explained from economic culture perspective – it was necessary to combine avariety of sources and evidence, and accordingly a different ways of description, analysis and interpretation.Apart from historical evidence and works of scholars dealing with socioeconomic aspects of Serbian societyand history two other sources of evidence were used: European Values Survey (EVS), and SoutheasternEuropean Social Study Project (SEESSP). This empircal evidence was analysed using cluster analysis inorder to explore legitimation patterns that corespond to cultural patterns in contemporary Serbian society.Recent empirical evidence was used to assess the role market as an institution plays in Serbian economicculture, and its relation to institutions of property and the state, as well as changes from XIX century onwards– to analyse how economic life of Serbian society was organised in this cultural-institutional triangle.From methodological and theoretical side legitimation mechanisms proved to be solid indicators of culturalpatterns, even if data used was not optimal. On the other hand, and not unexpected, introduction of marketmechanisms into a national economy turned out to be dependent on the context defined by existinginstitutional boundaries related to property and state organization, as well as more general kultural patternsand ethical norms. We cannot simply talk about introduction of market economy, but rather about specificmarket mechanisms and their structue and position in general economic practice of a society.Regarding Serbian society specifically, identified cultural patterns coincide with conclusions of other authorswhere egalitarian principles, collectivism and reliance on the state as a dominant economic player haveprominent role. Historical analysis also suggests that such a culture is not a result of many decades ofsocialism but rather its roots reach much farther into the past, as a constant common to different sociopoliticalsystems. Cultural patterns from the first decade of XXI century suggest legitimation deficit inrelation to the market. The market is not parceived as a mechanism appropriate for wealth distribution, andmajority of cultural patterns do not percieve market as a good criteria for inequalities regulation. Also, eventhough most cultural patterns suggest preference towards private property, the norm linked to accumulationand liberties to use property leads to ethical norm of Serbian society. Given the results, and althoughindirectly, it can be claimed with certainty that ethical norm of relative egalitarianism in functional (as themost appropriate mechanism to uphold and reproduce the norm) and legitimation (by establishing institutional interdependence) sense rely on the state as an institution – not the market. Long lastingtransitional uncertainity and lack of real reforms can be pointed at as reasons for identified situation inSerbian society and culture, as well as a cause of cognitively dissonant legitimation and cultural patterns.The research suggests conclusion in three main points: economic prosperity of a society requiresunambiguous cultural patterns which can provide clear guidance for economic action of an individual; one ofthe preconditions is stability of the framework in which economic life happens, something we can withcaution claim is the situation in Serbia today; and finally, apart from stability and clear value orientation,economic culture in Serbia depends equally on ability of society itself to eliminate cultural norms andpatterns for which there is a modern alternative. Apart from these conclusions theorietical framework andresults of this work by openning new questions present a solid ground for future research of economic culturein Serbia. 

Soit G un groupe de Lie résoluble connexe et H un de ses sous-groupes fermés connexes d'algèbres de Lie g et h respectivement. On note g* (resp. h*) le dual linéaire de g (resp. h) ). Le sujet de ma thèse consiste à étudier la restriction d'une série discrète π de G, associée à une orbite coadjointe Ω C g*, à H. Si la restriction de π à H se décompose en somme directe de représentations de H avec multiplicités finies, on dit que π est H-admissible. Notons Pg,n : Ω → h* l'application restriction. Il s'agit de démontrer la conjecture suivante due à Michel Duflo : 1. La représentation π est H-admissible si et seulement si l'application moment Pg,n est propre sur l'image. 2. Si π est H-admissible, et si T est une série discrète de H alors sa multiplicité dans la restriction de π à H doit pouvoir se calculer en « quantifiant » l'espace réduit correspondant (qui est compact dans ce cas). Dans cette thèse, nous apportons une réponse positive à cette conjecture dans deux situations, à savoir :(i) Le groupe G est résoluble exponentiel. (ii) Le groupe G est le produit semi direct d'un tore compact par le groupe de Heisenberg et H est un sous-groupe algébrique connexe
Let G be a connected solvable Lie group and H a closed connected subgroup with Lie algebra g and h respectively. We denote g* (resp. h*) the dual of g (resp. h). The aim of my thesis is to study the restriction of a discrete series π of G, associated with a coadjoint orbit Ω C g* to H. If the restriction of π to H can be decomposed in to a direct sum of representations of H with finite multiplicities, we say that π is H-admissible. Let Pg,n : Ω → h* denote the restriction map. My objective is to show the following conjecture due to Michel Duflo : 1. The representation π i s H-admissible if and only if the moment application Pg,n is proper on the image. 2. If π is H-admissible, and if T is a discrete series of H then it s multiplicity in the restriction of π to H must be calculated by « quantifying » the corresponding reduced space (that is compact in this case). In this thesis, we provide a positive response to this conjecture in two situations, namely when: (i) G is exponential solvable Lie group. (ii) G is the semi direct product of a compact torus and the Heisenberg group and H is a connected algebraic subgroup

Tam Chun Yu.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.
Includes bibliographical references (leaves 141-147).
Abstracts in English and Chinese.
Abstract --- p.I
Acknowledgements --- p.III
Table of Contents --- p.IV
List of Tables --- p.V
List of Figures --- p.VI
Chapter Chapter 1. --- Introduction --- p.1
Chapter Chapter 2. --- Literature Review --- p.5
Chapter 2.1 --- Real Estate Literature --- p.5
Chapter 2.2 --- Financial Literature --- p.6
Chapter 2.3 --- Impulse Response --- p.10
Chapter Chapter 3. --- Methodology --- p.12
Chapter 3.1 --- Augmented Dickey Fuller Test --- p.12
Chapter 3.2 --- GARCH Model --- p.14
Chapter 3.3 --- VAR Model --- p.16
Chapter Chapter 4. --- Data Description --- p.18
Chapter Chapter 5. --- Empirical Results --- p.20
Chapter 5.1 --- Overview for the Data Set --- p.21
Chapter 5.2 --- ADF Test --- p.22
Chapter 5.3 --- GARCH Model --- p.22
Chapter 5.4 --- VAR Model --- p.24
Chapter 5.5 --- Impulse Response (IR) --- p.34
Chapter Chapter 6. --- Conclusion --- p.38
Appendix 1. Variable Definition --- p.41
Appendix 2. Tables --- p.44
Appendix 3. Figures --- p.61
Appendix 4. Comparison of IR for different model in full sample case --- p.93
Appendix 5. Comparison of IR for different model in first sub period --- p.109
Appendix 6. Comparison of IR for different model in second sub period --- p.125
Bibliography --- p.141

In this thesis, we consider a new generalization of the Fourier transform, depending on four complex parameters and all the powers of the Fourier transform. This new transform is studied in some Lebesgue spaces. In fact, taking into account the values of the parameters of the operator, we can have very different kernels and so, the corresponding operator is studied in different Lebesgue spaces, accordingly with its kernel. We begin with the characterization of each operator by its characteristic polynomial. This characterization serves as a basis for the study of the forthcoming properties. Following this, we present, for each case, the spectrum of the corresponding operator, necessary and sufficient conditions for which the operator is invertible, Parseval-type identities and conditions for which the operator is unitary and an involution of order n. After this, we contruct new convolutions associated with those operators and obtain the corresponding factorization identities and some norm inequalities. By using these new operators and convolutions, we construct new integral equations and study their solvability. In this sense, we have equations generated by the studied operators and also a class of equations of convolution-type depending on multi-dimensional Hermite functions. Furthermore, we study the solvability of classical integral equations, using the new operators and convolutions, namely a class of Wiener-Hopf plus Hankel equations, whose solution is written in terms of a Fourier-type series. For one case of this generalization of the Fourier transform, that only depends on the cosine and sine Fourier transforms, we obtain PaleyWiener and Wiener’s Tauberian results, using the associated convolution and a new translation induced by that convolution. Heisenberg uncertainty principles for the one-dimensional case and for the multi-dimensional case are obtained for a particular case of the introduced operator. At the end, as an application outside of mathematics, we obtain a new result in signal processing, more properly, in a filtering processing, by applying one of our new convolutions.
Nesta tese, consideramos uma nova generalização da transformação de Fourier, dependente de quatro parâmetros complexos e de todas as potências da transformação de Fourier. Esta nova transformação é estudada em alguns espaços de Lebesgue. De facto, tendo em conta os valores dos parâmetros, podemos ter núcleos muito diferentes e assim, o correspondente operador é estudado em diferentes espaços de Lebesgue, de acordo com o seu núcleo. Começamos com a caracterização de cada operador pelo seu polinómio característico. Esta caracterização serve de base para o estudo das propriedades seguintes. Seguindo isto, apresentamos, para cada caso, o espetro do correspondente operador, condições necessárias e suficientes para as quais o operador é invertível, identidades do tipo de Parseval e condições para as quais o operador é unitário e uma involução de ordem n. Depois disto, construímos novas convoluções associadas àqueles operadores e obtemos as correspondentes identidades de factorização e algumas desigualdades da norma. Usando estes novos operadores e convoluções, construímos novas equações integrais e estudamos a sua solvabilidade. Neste sentido, temos equações geradas pelos operadores estudados e também uma classe de equações do tipo de convolução dependendo de funções de Hermite multidimensionais. Além disso, estudamos a solvabilidade de equações integrais clássicas, usando os novos operadores e convoluções, nomeadamente uma classe de equações de Wiener-Hopf mais Hankel, cuja solução é escrita em termos de uma série do tipo de Fourier. Para um caso desta generalização da transformação de Fourier, que depende apenas das transformações de Fourier do cosseno e do seno, obtemos resultados de Paley-Wiener e resultados Tauberianos de Wiener, usando a convolução associada e uma nova translação induzida por essa convolução. Princípios de incerteza de Heisenberg para os casos unidimensional e multidimensional são obtidos para um caso particular do operador introduzido. No final, como uma aplicação fora da matemática, obtemos um novo resultado em processamento de sinal, mais propriamente, num processo de filtragem, por aplicação de uma das nossas novas convoluções.
Programa Doutoral em Matemática Aplicada