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Добірка наукової літератури з теми "Holomorphic functional calculi"

Автор: Grafiati
Опубліковано: 10 грудня 2022
Оновлено: 28 січня 2023

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Статті в журналах з теми "Holomorphic functional calculi"

1

Haase, Markus. "A GENERAL FRAMEWORK FOR HOLOMORPHIC FUNCTIONAL CALCULI." Proceedings of the Edinburgh Mathematical Society 48, no. 2 (May 23, 2005): 423–44. http://dx.doi.org/10.1017/s0013091504000513.

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AbstractWe present an abstract approach to the construction of holomorphic functional calculi for unbounded operators and apply it to the special case of sectorial operators. In effect, we obtain a calculus for a much larger class of functions than was known before, including certain meromorphic functions. We discuss the role of topology. Then we prove in detail a composition rule $(f\circ g)(A)=f(g(A))$ which is the main result of the paper. This is done in such a way that the proof can easily be transferred to functional calculi for other classes of operators.
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2

HAASE, MARKUS. "SPECTRAL MAPPING THEOREMS FOR HOLOMORPHIC FUNCTIONAL CALCULI." Journal of the London Mathematical Society 71, no. 03 (May 24, 2005): 723–39. http://dx.doi.org/10.1112/s0024610705006538.

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3

Albrecht, David, Edwin Franks, and Alan McIntosh. "Holomorphic functional calculi and sums of commuting opertors." Bulletin of the Australian Mathematical Society 58, no. 2 (October 1998): 291–305. http://dx.doi.org/10.1017/s0004972700032251.

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Let S and T be commuting operators of type ω and type ϖ in a Banach space X. Then the pair has a joint holomorphic functional calculus in the sense that it is possible to define operators f(S, T) in a consistent manner, when f is a suitable holomorphic function defined on a product of sectors. In particular, this gives a way to define the sum S + T when ω + ϖ < π. We show that this operator is always of type μ where μ = max{ω, ϖ}. We explore when bounds on the individual functional calculi of S and T imply bounds on the functional calculus of the pair (S, T), and some implications for the regularity problem of when ∥(S + T)u∥ is equivalent to ∥Su∥ + ∥Tu∥.
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4

Auscher, P., A. McIntosh, and A. Nahmod. "Holomorphic functional calculi of operators, quadratic estimates and interpolation." Indiana University Mathematics Journal 46, no. 2 (1997): 0. http://dx.doi.org/10.1512/iumj.1997.46.1180.

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5

Franks, Edwin, and Alan McIntosh. "Discrete quadratic estimates and holomorphic functional calculi in Banach spaces." Bulletin of the Australian Mathematical Society 58, no. 2 (October 1998): 271–90. http://dx.doi.org/10.1017/s000497270003224x.

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We develop a discrete version of the weak quadratic estimates for operators of type w explained by Cowling, Doust, McIntosh and Yagi, and show that analogous theorems hold. The method is direct and can be generalised to the case of finding necessary and sufficient conditions for an operator T to have a bounded functional calculus on a domain which touches σ(T) nontangentially at several points. For operators on Lp, 1 < p < ∞, it follows that T has a bounded functional calculus if and only if T satisfies discrete quadratic estimates. Using this, one easily obtains Albrecht's extension to a joint functional calculus for several commuting operators. In Hilbert space the methods show that an operator with a bounded functional calculus has a uniformly bounded matricial functional calculus.The basic idea is to take a dyadic decomposition of the boundary of a sector Sv. Then on the kth ingerval consider an orthonormal sequence of polynomials . For h ∈ H∞(Sν), estimates for the uniform norm of h on a smaller sector Sμ are obtained from the coefficients akj = (h, ek, j). These estimates are then used to prove the theorems.
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6

DUONG, Xuan Thinh, and Lixin YAN. "Weighted inequalities for holomorphic functional calculi of operators with heat kernel bounds." Journal of the Mathematical Society of Japan 57, no. 4 (October 2005): 1129–52. http://dx.doi.org/10.2969/jmsj/1150287306.

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7

Duong, Xuan Thinh, and Lixin Yan. "Commutators of BMO functions and singular integral operators with non-smooth kernels." Bulletin of the Australian Mathematical Society 67, no. 2 (April 2003): 187–200. http://dx.doi.org/10.1017/s0004972700033669.

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Let χ be a space of homogeneous type of infinite measure. Let T be a singular integral operator which is bounded on Lp (χ) for some p, 1 < p < ∞. We give a sufficient condition on the kernel of T so that when a function b ∈ BMO(χ), the commutator [b, T](f) = T (bf) – bT (f) is bounded on Lp spaces for all p, 1 < p > ∞. Our condition is weaker than the usual Hörmander condition. Applications include Lp-boundedness of the commutators of BMO functions and holomorphic functional calculi of Schrödinger operators, and divergence form operators on irregular domains.
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8

GHILONI, RICCARDO, VALTER MORETTI, and ALESSANDRO PEROTTI. "CONTINUOUS SLICE FUNCTIONAL CALCULUS IN QUATERNIONIC HILBERT SPACES." Reviews in Mathematical Physics 25, no. 04 (May 2013): 1350006. http://dx.doi.org/10.1142/s0129055x13500062.

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The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic C*-algebras and to define, on each of these C*-algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.
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9

Batty, Charles, Alexander Gomilko, and Yuri Tomilov. "A Besov algebra calculus for generators of operator semigroups and related norm-estimates." Mathematische Annalen, November 12, 2019. http://dx.doi.org/10.1007/s00208-019-01924-2.

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Abstract We construct a new bounded functional calculus for the generators of bounded semigroups on Hilbert spaces and generators of bounded holomorphic semigroups on Banach spaces. The calculus is a natural (and strict) extension of the classical Hille–Phillips functional calculus, and it is compatible with the other well-known functional calculi. It satisfies the standard properties of functional calculi, provides a unified and direct approach to a number of norm-estimates in the literature, and allows improvements of some of them.
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10

Hussein, Shawgy, Simon Joseph, Ahmed Sufyan, Murtada Amin, Ranya Tahire, and Hala Taha. "Functional Calculus for the Series of Semigroup Generators Via Transference." Global Journal of Science Frontier Research, December 23, 2019, 57–84. http://dx.doi.org/10.34257/gjsfrfvol19is5pg57.

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In this paper, apply an established transference principle to obtain the boundedness of certain functional calculi for the sequence of semigroup generators. It is proved that if be the sequence generates 0- semigroups on a Hilbert space, then for each the sequence of operators has bounded calculus for the closed ideal of bounded holomorphic functions on right half–plane. The bounded of this calculus grows at most logarithmically as. As a consequence decay at ∞. Then showed that each sequence of semigroup generator has a so-called (strong) m-bounded calculus for all m∈ℕ, and that this property characterizes the sequence of semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-called semigroups, the Hilbert space results actually hold in general Banach spaces.
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Дисертації з теми "Holomorphic functional calculi"

1

Schippers, Eric. "The calculus of conformal metrics and univalence criteria for holomorphic functions." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0021/NQ45740.pdf.

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2

Pannasch, Florian [Verfasser], Markus [Akademischer Betreuer] Haase, and Detlef [Gutachter] Müller. "The Holomorphic Hörmander Functional Calculus / Florian Pannasch ; Gutachter: Detlef Müller ; Betreuer: Markus Haase." Kiel : Universitätsbibliothek Kiel, 2019. http://d-nb.info/1202630561/34.

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3

Pannasch, Florian Verfasser], Markus [Akademischer Betreuer] [Haase, and Detlef [Gutachter] Müller. "The Holomorphic Hörmander Functional Calculus / Florian Pannasch ; Gutachter: Detlef Müller ; Betreuer: Markus Haase." Kiel : Universitätsbibliothek Kiel, 2019. http://d-nb.info/1202630561/34.

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4

Stahlhut, Sebastian. "Problèmes aux limites pour les systèmes elliptiques." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112186.

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Dans cette thèse, nous étudions des problèmes aux limites pour les systèmes elliptiques sous forme divergence avec coefficients complexes dans L^{infty}. Nous prouvons des estimations a priori, discutons de la solvabilité et d'extrapolation de la solvabilité. Nous utilisons une transformation via des équations Cauchy-Riemann généralisées due à P. Auscher, A. Axelsson et A. McIntosh. On peut résoudre les équations Cauchy-Riemann généralisées via la semi-groupe engendré par un opérateur différentiel perturbé d'ordre un de type Dirac. A l'aide du semi-groupe, nous étudions la théorie L^{p} avec une discussion sur la bisectorialité, le calcul fonctionnel holomorphe et les estimations hors-diagonales pour des opérateurs dans le calcul fonctionnel. En particulier, nous développons une théorie L^{p}-L^{q} pour des opérateurs dans le calcul fonctionnel d'opérateur de type Dirac perturbé. Les problèmes de Neumann, Régularité et Dirichlet se formulent avec des estimations quadratiques et des estimations pour la fonction maximale nontangentielle. Cela conduit à à démontrer de telles estimations pour le semi-groupe d'opérateur de Dirac Pour cela, nous utilisons les espaces Hardy associés et les identifions dans certains cas avec des sous-espaces des espaces de Hardy et Lebesgue classiques. Nous obtenons enfin des estimations a priori pour les problème aux limites via une extension utilisant des espaces de Sobolev associés. Nous utilisons les estimations a priori pour une discussion sur la solvabilité des problèmes aux limites et montrer un théorème d'extrapolation de la solvabilité
In this this thesis we study boundary value problems for elliptic systems in divergence form with complex coefficients in L^{\infty}. We prove a priori estimates, discuss solvability and extrapolation of solvability. We use a transformation to generalized Cauchy-Riemann equations due to P. Auscher, A. Axelsson, and A. McIntosh. The generalized Cauchy-Riemann equations can be solved by the semi-group generated by a perturbed first order Dirac/differential operator. In relation to semi-group theory we setup the L^p theory by a discussion of bisectoriality, holomorphic functional calculus and off-diagonal estimates for operators in the functional calculus. In particular, we develop an L^p-L^q theory for operators in the functional calculus of the first order perturbed Dirac/differential operators. The formulation of Neumann, Regularity and Dirichlet problems involve square function estimates and nontangential maximal function estimates. This leads us to discuss square function estimates and nontangential maximal function estimates involving operators in the functional calculus of the perturbed first order Dirac/differential operator. We discuss the related Hardy spaces associated to operators and prove identifications by subspaces of classical Hardy and Lebesgue spaces. We obtain the a priori estimates by an extension of the square function estimates and nontangential maximal function estimates to Sobolev spaces associated to operators. We use the a priori estimates for a discussion of solvability and extrapolation of solvability
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5

Morris, Andrew Jordan. "Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds." Phd thesis, 2010. http://hdl.handle.net/1885/8864.

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The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to the theory of differential operators. This is a generalization of the connection between Littlewood--Paley--Stein estimates and the functional calculus provided by the Fourier transform. We use the former approach in this thesis to study first-order differential operators on Riemannian manifolds. The theory developed is local in the sense that it does not depend on the spectrum of the operator in a neighbourhood of the origin. When we apply harmonic analysis to obtain estimates, the local theory only requires that we do so up to a finite scale. This allows us to consider manifolds with exponential volume growth in situations where the global theory requires polynomial volume growth. A holomorphic functional calculus is constructed for operators on a reflexive Banach space that are bisectorial except possibly in a neighbourhood of the origin. We prove that this functional calculus is bounded if and only if certain local quadratic estimates hold. For operators with spectrum in a neighbourhood of the origin, the results are weaker than those for bisectorial operators. For operators with a spectral gap in a neighbourhood of the origin, the results are stronger. In each case, however, local quadratic estimates are a more appropriate tool than standard quadratic estimates for establishing that the functional calculus is bounded. This theory allows us to define local Hardy spaces of differential forms that are adapted to a class of first-order differential operators on a complete Riemannian manifold with at most exponential volume growth. The local geometric Riesz transform associated with the Hodge--Dirac operator is bounded on these spaces provided that a certain condition on the exponential growth of the manifold is satisfied. A characterisation of these spaces in terms of local molecules is also obtained. These results can be viewed as the localisation of those for the Hardy spaces of differential forms introduced by Auscher, McIntosh and Russ. Finally, we introduce a class of first-order differential operators that act on the trivial bundle over a complete Riemannian manifold with at most exponential volume growth and on which a local Poincar\'{e} inequality holds. A local quadratic estimate is established for certain perturbations of these operators. As an application, we solve the Kato square root problem for divergence form operators on complete Riemannian manifolds with Ricci curvature bounded below that are embedded in Euclidean space with a uniformly bounded second fundamental form. This is based on the framework for Dirac type operators that was introduced by Axelsson, Keith and McIntosh.
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Книги з теми "Holomorphic functional calculi"

1

Analysis II: Differential and Integral Calculus, Fourier Series, Holomorphic Functions. Springer London, Limited, 2006.

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2

k-Schur Functions and Affine Schubert Calculus. Springer, 2014.

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3

Lam, Thomas, Luc Lapointe, Jennifer Morse, Anne Schilling, and Mark Shimozono. K-Schur Functions and Affine Schubert Calculus. Springer, 2014.

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4

Lam, Thomas, Luc Lapointe, Jennifer Morse, Anne Schilling, Mark Shimozono, and Mike Zabrocki. k-Schur Functions and Affine Schubert Calculus. Springer, 2016.

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5

Godement, Roger. Analyse mathématique IV: Intégration et théorie spectrale, analyse harmonique, le jardin des délices modulaires. Springer, 2003.

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6

Schippers, Eric. The calculus of conformal metrics and univalence criteria for holomorphic functions. 1999, 1999.

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7

Schippers, Eric. The calculus of conformal metrics and univalence criteria for holomorphic functions. 1999.

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8

(Translator), P. Spain, ed. Analysis II: Differential and Integral Calculus, Fourier Series, Holomorphic Functions (Universitext). Springer, 2005.

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9

Godement, Roger. Analyse mathématique II: Calcul différentiel et intégral, séries de Fourier, fonctions holomorphes. 2nd ed. Springer, 1992.

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10

Ransford, Thomas, Javad Mashreghi, Omar El-Fallah, and Karim Kellay. Primer on the Dirichlet Space. Cambridge University Press, 2013.

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Частини книг з теми "Holomorphic functional calculi"

1

deLaubenfels, Ralph. "Holomorphic C-existence families." In Existence Families, Functional Calculi and Evolution Equations, 128–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073422.

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2

deLaubenfels, Ralph. "Boundary values of holomorphic semigroups." In Existence Families, Functional Calculi and Evolution Equations, 73–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073411.

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3

deLaubenfels, Ralph. "Unbounded holomorphic functional calculus for operators with polynomially bounded resolvents." In Existence Families, Functional Calculi and Evolution Equations, 133–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073423.

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4

Karpfinger, Christian. "Holomorphic Functions." In Calculus and Linear Algebra in Recipes, 893–904. Berlin, Heidelberg: Springer Berlin Heidelberg, 2022. http://dx.doi.org/10.1007/978-3-662-65458-3_80.

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5

Gürlebeck, Klaus, Klaus Habetha, and Wolfgang Sprößig. "Operator calculus." In Application of Holomorphic Functions in Two and Higher Dimensions, 95–150. Basel: Springer Basel, 2016. http://dx.doi.org/10.1007/978-3-0348-0964-1_4.

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6

Weis, Lutz. "The H ∞Holomorphic Functional Calculus for Sectorial Operators — a Survey." In Partial Differential Equations and Functional Analysis, 263–94. Basel: Birkhäuser Basel, 2006. http://dx.doi.org/10.1007/3-7643-7601-5_16.

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7

Delaubenfels, Ralph. "Boundary Values of Holomorphic Semigroups, H∞ Functional Calculi, and the Inhomogeneous Abstract Cauchy Problem." In differential equations in Banach spaces, 181–94. CRC Press, 2020. http://dx.doi.org/10.1201/9781003072102-14.

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8

"Holomorphic Functional Calculus." In Ultrametric Banach Algebras, 135–41. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812775603_0023.

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9

"Holomorphic Functional Calculus." In Banach Algebras of Ultrametric Functions, 203–21. WORLD SCIENTIFIC, 2022. http://dx.doi.org/10.1142/9789811251665_0008.

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10

"An(2) and Calculus of Variations for Harmonic and for Holomorphic Functions in U." In The Krzyż Conjecture: Theory and Methods, 149–52. WORLD SCIENTIFIC, 2021. http://dx.doi.org/10.1142/9789811226380_0025.

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