Academic literature on the topic 'Clifford analysis'
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Journal articles on the topic "Clifford analysis"
Leutwiler, Heinz. "Modified clifford analysis." Complex Variables, Theory and Application: An International Journal 17, no. 3-4 (February 1992): 153–71. http://dx.doi.org/10.1080/17476939208814508.
Full textRyan, John. "Duality in complex Clifford analysis." Journal of Functional Analysis 61, no. 2 (April 1985): 117–35. http://dx.doi.org/10.1016/0022-1236(85)90031-x.
Full textEriksson-Bique, Sirkka-Liisa. "On modified clifford analysis." Complex Variables, Theory and Application: An International Journal 45, no. 1 (July 2001): 11–33. http://dx.doi.org/10.1080/17476930108815366.
Full textRen, Guangbin, Haiyan Wang, and Lin Chen. "Paracomplex Hermitean Clifford Analysis." Complex Analysis and Operator Theory 8, no. 6 (November 23, 2013): 1367–82. http://dx.doi.org/10.1007/s11785-013-0341-3.
Full textChen, Lin, Guangbin Ren, and Haiyan Wang. "Bicomplex Hermitian Clifford analysis." Frontiers of Mathematics in China 10, no. 3 (February 2, 2015): 523–46. http://dx.doi.org/10.1007/s11464-015-0410-1.
Full textSommen, F., and W. Sprößig. "Introduction to Clifford analysis." Mathematical Methods in the Applied Sciences 25, no. 16-18 (November 10, 2002): 1337–42. http://dx.doi.org/10.1002/mma.373.
Full textTimorin, V. A. "Circles and Clifford Algebras." Functional Analysis and Its Applications 38, no. 1 (January 2004): 45–51. http://dx.doi.org/10.1023/b:faia.0000024867.02438.e3.
Full textVasilescu, Florian-Horia. "Spectrum and Analytic Functional Calculus for Clifford Operators via Stem Functions." Concrete Operators 8, no. 1 (January 1, 2021): 90–113. http://dx.doi.org/10.1515/conop-2020-0115.
Full textRen, Guangbin, Lin Chen, and Haiyan Wang. "Split-quaternionic Hermitian Clifford analysis." Complex Variables and Elliptic Equations 60, no. 3 (August 26, 2014): 333–53. http://dx.doi.org/10.1080/17476933.2014.936861.
Full textKrausshar, Rolf Sören. "Automorphic Forms in Clifford Analysis." Complex Variables, Theory and Application: An International Journal 47, no. 5 (May 2002): 417–40. http://dx.doi.org/10.1080/02781070290013758.
Full textDissertations / Theses on the topic "Clifford analysis"
Faustino, Nelson José Rodrigues. "Discrete Clifford analysis." Doctoral thesis, Universidade de Aveiro, 2009. http://hdl.handle.net/10773/2942.
Full textEsta tese estuda os fundamentos de uma teoria discreta de funções em dimensões superiores usando a linguagem das Álgebras de Clifford. Esta abordagem combina as ideias do Cálculo Umbral e Formas Diferenciais. O potencial desta abordagem assenta essencialmente da osmose entre ambas as linguagens. Isto permitiu a construção de operadores de entrelaçamento entre estruturas contínuas e discretas, transferindo resultados conhecidos do contínuo para o discreto. Adicionalmente, isto resultou numa transcrição mimética de bases de polinómios, funções geradoras, Decomposição de Fischer, Lema de Poincaré, Teorema de Stokes, fórmula de Cauchy e fórmula de Borel-Pompeiu. Esta teoria também inclui a descrição dos homólogos discretos de formas diferenciais, campos vectores e integração discreta. De facto, a construção resultante de formas diferenciais, campos vectores e integração discreta em termos de coordenadas baricêntricas conduz à correspondência entre a teoria de Diferenças Finitas e a teoria de Elementos Finitos, dando um núcleo de aplicações desta abordagem promissora em análise numérica. Algumas ideias preliminares deste ponto de vista foram apresentadas nesta tese. Também foram apresentados resultados preliminares na teoria discreta de funções em complexos envolvendo simplexes. Algumas ligações com Combinatória e Mecânica Quântica foram também apresentadas ao longo desta tese.
This thesis studies the fundamentals of a higher dimensional discrete function theory using the Clifford Algebra setting. This approach combines the ideas of Umbral Calculus and Differential Forms. Its powerful rests mostly on the interplay between both languages. This allowed the construction of intertwining operators between continuous and discrete structures, lifting the well known results from continuum to discrete. Furthermore, this resulted in a mimetic transcription of basis polynomial, generating functions, Fischer Decomposition, Poincaré and dual-Poincaré lemmata, Stokes theorem and Cauchy’s formula. This theory also includes the description discrete counterparts of differential forms, vector-fields and discrete integration. Indeed the resulted construction of discrete differential forms, discrete vector-fields and discrete integration in terms of barycentric coordinates leads to the correspondence between the theory of Finite Differences and the theory of Finite Elements, which gives a core of promising applications of this approach in numerical analysis. Some preliminary ideas on this point of view were presented in this thesis. We also developed some preliminary results in the theory of discrete monogenic functions on simplicial complexes. Some connections with Combinatorics and Quantum Mechanics were also presented along this thesis.
Gomes, Narciso Resende. "Compressive sensing in Clifford analysis." Doctoral thesis, Universidade de Aveiro, 2015. http://hdl.handle.net/10773/15170.
Full textCompressed sensing is a new paradigm in signal processing which states that for certain matrices sparse representations can be obtained by a simple l1-minimization. In this thesis we explore this paradigm for higher-dimensional signal. In particular three cases are being studied: signals taking values in a bicomplex algebra, quaternionic signals, and complex signals which are representable by a nonlinear Fourier basis, a so-called Takenaka-Malmquist system.
Amostragem Compressiva é um novo paradigma em processamento de sinal, no qual se assegura, para determinadas matrizes, que as representações esparsas de sinais podem ser obtidas por intermédio de um simples procedimento de l1-minimização. Nesta tese, exploramos este paradigma para sinais em dimensões superiores. Estudaremos três casos particulares: sinais com valores na álgebra bi-complexa, sinais quaterniónicos e, finalmente, sinais complexos representáveis por uma base de Fourier não-linear, dito sistema de Takenaka-Malmquist.
Otto, Heinz. "Cauchy-Pompeiusche Integraldarstellungen in der Clifford-Analysis." [S.l.] : [s.n.], 2006. http://www.diss.fu-berlin.de/2006/384/index.html.
Full textMendes, Douglas 1985. "Álgebras de Clifford e a fibração de Hopf." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306400.
Full textDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Os grupos Spin aparecem de várias formas em Matemática e em Física-Matemática, tendo grande importância na teoria de brados e de operadores diferenciais sobre os mesmos. O conceito de estrutura spin é deles derivado, sendo ele a base de toda uma teoria, conhecida como geometria spin. Esta dissertação introduz os primeiros conceitos necessários ao estudo de tais grupos, assim como alguns aspectos importantes relacionados a eles. Dada a natureza dos grupos Spin e dos problemas aos quais estão relacionados, vários tópicos na interface entre álgebra e geometria tiveram de ser abordados. Estudamos em um primeiro momento as álgebras de Clifford, sua representação adjunta torcida e os grupos Spin como subgrupos do grupo das unidades de tais álgebras. À estes estudos, seguiu-se uma análise detalhada da teoria de espaços de recobrimento e da classificação dos mesmos. Pudemos com isso entender o grupo Spin, via representação adjunta torcida, como o recobrimento universal do grupo especial ortogonal de um espaço quadrático não-degenerado. Nos concentramos daí na teoria de brados principais e a relação destes com as propriedades geométricas das variedades sobre as quais eles estão construídos. Para sintetizar o que foi estudado, construímos algebricamente a fibração de Hopf ao final desta dissertação, explicitando sua relação com a estrutura spin da esfera S²
Abstract: Spin groups come in many forms in Mathematics and Mathematical Physics, having great importance in the theory of fiber bundles and differential operators defined on them. The concept of spin structure is derived from them, being the basis of all a theory, known as spin geometry. This thesis introduces the first concepts necessary for the study of such groups, as well as important aspects related to them. Given the nature of the Spin groups and problems which they're related to, several topics at the interface between algebra and geometry had to be addressed. At first, we studied Clifford algebras, their twisted adjoint representation and Spin groups as subgroups of the group of units of such algebras. Followed these studies a detailed analysis of the theory of covering spaces and the classification of them. Done that, we were able to understand the group Spin, via the twisted adjoint representation, as the universal covering space of the special orthogonal group of a non-degenerate quadratic space. From there, we focused on the theory of principal bundles and their relationship with the geometric properties of manifolds on which they are built. To summarize what was studied, we algebraically construct the Hopf fibration at the end of this thesis, explaining its relationship with the spin structure of the sphere S²
Mestrado
Matematica
Mestre em Matemática
Kou, Kit Ian. "Paley-Wiener theorem and Shannon sampling with the Clifford analysis setting." Thesis, University of Macau, 2005. http://umaclib3.umac.mo/record=b2492153.
Full textMattos, Eduardo Souza. "Sobre álgebras de Clifford, geometria projetiva e visão computacional." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307238.
Full textDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Atualmente, o estudo das Álgebras de Clifford é utilizado em inúmeras áreas de pesquisa. Uma delas é na área de Visão Computacional. O objetivo central dessa dissertação consiste em exibir noções sobre Álgebras de Clifford e sua utilização na formulação dos conceitos e definições de operações entre objetos da Geometria Projetiva e na formulação algébrica de câmeras virtuais, que é um dos assuntos tratados na área de Visão Computacional. Para isso são expostos de forma gradual e coerente os principais aspectos teóricos necessários para atingir os objetivos citados. Como resultado, as Álgebras de Clifford proporcionam uma excelente descrição da Geometria Projetiva e das câmeras virtuais
Abstract: Currently, the study of Clifford algebras are used in many research areas. One is in the area of Computer Vision. The main objective of this dissertation is to display notions of Clifford algebras and their use in formulating the concepts and definitions of transactions between objects of Projective Geometry and algebraic formulation of virtual cameras, which is one of the topics covered in Computer Vision. For it is exposed gradually and consistently the main theoretical aspects needed to achieve the goals mentioned. As a result, Clifford algebras provide an excellent description of Projective Geometry and virtual cameras
Mestrado
Matematica Aplicada
Mestre em Matemática Aplicada
Liu, Shuang. "Convergence of Fourier series on the sphere in the Clifford analysis setting." Thesis, University of Macau, 2002. http://umaclib3.umac.mo/record=b1446719.
Full textResende, Adriana Souza. "Introdução elementar às álgebras Clifford 'CL IND.2' 'CL IND. 3'." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306698.
Full textDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatistica e Computação Cientifica
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Resumo: O presente trabalho tem a intenção de apresentar por intermédio de uma linguagem unificada alguns conceitos de cálculo vetorial, álgebra linear (matrizes e transformações lineares) e também algumas idéias elementares sobre os grupos de rotações em duas e três dimensões e seus grupos de recobrimento, que geralmente são tratados como "fragmentos" em várias modalidades de cursos no ensino superior. Acreditamos portanto que nosso texto possas ser útil para alunos dos cursos de graduação dos cursos de Engenharia, Física, Matemática e interessados em Matemática em geral. A linguagem unificada à que nos referimos acima é obtida com a introdução do conceitos das álgebras geométricas (ou de Clifford) onde, como veremos, é possível fornecer uma formulação algébrica elegante aos conceitos de vetores, planos e volumes orientados e definir para tais objetos o produto escalar, os produtos contraídos à esquerda e à direita, o produto exterior (associado, como veremos, em casos particulares ao produto vetorial) e finalmente o produto geométrico (Clifford), o que permite o uso desses conceitos para a solução de inúmeros problemas de geometria analítica no R ² e no R ³. Procuramos ilustrar todos estes conceitos com vários exemplos e exercícios com graus variáveis de dificuldades. Nossa apresentação é bem próxima àquela do livro de Lounesto, e de fato muitas seções são traduções (eventualmente seguidas de comentários) de seções daquele livro. Contudo, em muitos lugares, acreditamos que nossa apresentação esclarece e completa as correspondentes do livro de Lounesto
Abstract: This paper aims to present using an unified language a few concepts of vector calculus, linear algebra (matrices and linear transformations) and also some basic ideas about the groups of rotations in two and three dimensions and their covering group, which generally are treated as "fragments" in various types of courses in higher education. We believe therefore that our text should be useful to students of undergraduate courses like Engineering, Physics, Mathematics and people interested in Mathematics in general. The unified language that we refer to above is obtained by introducing the concept of geometric (or Clifford) algebra where, as we shall see, it is possible to give an elegant algebraic formulation to the concepts of vectors, oriented planes and oriented volumes, and to define to those objects the scalar product, the right and left contracted products, the exterior product (associated, as we shall see, in particular cases to the vector product) and finally the geometric (Clifford) product, and moreover, to use those concepts to solve may problems of analytic geometry in R ² and R ³. We illustrated all those concepts with several examples and exercises with variable degrees of difficulties. Our presentation is nearly the one in Lounesto's book, and in fact some sections are no more than translations (eventually with commentaries) from sections of that book. However, in many places, we believe that our presentation clarify nd completement the corresponding ones in Lounesto's book
Mestrado
Ágebra
Mestre em Matemática
Wainer, Samuel Augusto 1989. "Geometria riemanniana e semi-riemanniana no fibrado de Clifford e aplicações." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305959.
Full textDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: O resumo poderá ser visualizado no texto completo da tese digital
Abstract: The complete abstract is available with the full electronic document .
Mestrado
Matematica
Mestre em Matemática
Van, Vuren Lennard Clifford. "Local economic development in the Emfuleni municipal area : a critical analysis / Lennard Clifford van Vuren." Thesis, North-West University, 2003. http://hdl.handle.net/10394/2436.
Full textBooks on the topic "Clifford analysis"
Bernstein, Swanhild, ed. Topics in Clifford Analysis. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23854-4.
Full textKrausshar, Rolf Soren. Eisenstein series in Clifford analysis. Aachen: Wissenschaftsverlag Mainz, 2000.
Find full textCerejeiras, Paula, Craig A. Nolder, John Ryan, and Carmen Judith Vanegas Espinoza, eds. Clifford Analysis and Related Topics. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-00049-3.
Full textBrackx, F., J. S. R. Chisholm, and V. Souček, eds. Clifford Analysis and Its Applications. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0862-4.
Full textYing, Qiao Yu, and Wen Guo Chun, eds. Real and complex Clifford analysis. [New York]: Springer, 2006.
Find full textF, Brackx, Chisholm J. S. R, Souček V, North Atlantic Treaty Organization. Scientific Affairs Division., and NATO Advanced Research Workshop on Clifford Analysis and Its Applications (2000 : Prague, Czech Republic), eds. Clifford analysis and its applications. Dordrecht: Kluwer Academic, 2001.
Find full textBrackx, F. Clifford Analysis and Its Applications. Dordrecht: Springer Netherlands, 2001.
Find full textLounesto, Pertti. Clifford algebras and spinors. Cambridge: Cambridge University Press, 1997.
Find full textClifford algebras and spinors. 2nd ed. Cambridge: Cambridge University Press, 2001.
Find full textRyan, John. Clifford Algebras and their Applications in Mathematical Physics: Volume 2: Clifford Analysis. Boston, MA: Birkhäuser Boston, 2000.
Find full textBook chapters on the topic "Clifford analysis"
Arfaoui, Sabrine, Anouar Ben Mabrouk, and Carlo Cattani. "Clifford wavelets." In Wavelet Analysis, 51–98. Boca Raton : Chapman & Hall/CRC Press, 2021.: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003096924-4.
Full textRyan, John. "Clifford Analysis." In Lectures on Clifford (Geometric) Algebras and Applications, 53–89. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8190-6_3.
Full textRosén, Andreas. "Clifford Algebra." In Geometric Multivector Analysis, 73–103. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31411-8_3.
Full textKähler, Uwe, and Nelson Vieira. "Fractional Clifford Analysis." In Trends in Mathematics, 191–201. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-08771-9_13.
Full textJefferies, Brian. "3. Clifford Analysis." In Lecture Notes in Mathematics, 27–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-70746-2_3.
Full textSabadini, Irene, and Frank Sommen. "Hermitian Clifford Analysis." In Operator Theory, 1581–608. Basel: Springer Basel, 2015. http://dx.doi.org/10.1007/978-3-0348-0667-1_13.
Full textKähler, Uwe, and Frank Sommen. "Discrete Clifford Analysis." In Operator Theory, 1609–30. Basel: Springer Basel, 2015. http://dx.doi.org/10.1007/978-3-0348-0667-1_18.
Full textSommen, Frank, and Hennie De Schepper. "Introductory Clifford Analysis." In Operator Theory, 1339–67. Basel: Springer Basel, 2015. http://dx.doi.org/10.1007/978-3-0348-0667-1_29.
Full textSabadini, Irene M., and Frank Sommen. "Hermitian Clifford Analysis." In Operator Theory, 1–26. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0692-3_13-1.
Full textKaehler, Uwe, and Frank Sommen. "Discrete Clifford Analysis." In Operator Theory, 1–19. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0692-3_18-1.
Full textConference papers on the topic "Clifford analysis"
Sommen, Franciscus C. "Clifford superanalysis." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825548.
Full textRen, Guangbin, and Liang Liu. "Berezin Transform in Clifford Analysis." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991011.
Full textSommen, F., Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Micro-localisation from Clifford Analysis." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636660.
Full text"Clifford and Quaternion Analysis." In Proceedings of the 6th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812837332_others03.
Full text"Clifford and quaternion analysis." In Proceedings of the 7th International ISAAC Congress. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814313179_others04.
Full textSommen, F., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Haar Wavelets is a Clifford Algebra." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790266.
Full textBrackx, F., H. De Schepper, D. Eelbode, and V. Souček. "Differential Forms in Hermitean Clifford Analysis." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991008.
Full textMalonek, H. R., and M. I. Falcão. "Clifford Analysis between Continuous and Discrete." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991019.
Full textGürlebeck, Klaus, Wolfgang Sprössig, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Analysis in Clifford Algebras—Some Aspects." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636713.
Full textBEGEHR, H. "REPRESENTATION FORMULAS IN CLIFFORD ANALYSIS." In Proceedings of the International Conference to Celebrate Robert P Gilbert's 70th Birthday. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704405_0003.
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