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Relevant bibliographies by topics / Bergman kernel functions

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Academic literature on the topic 'Bergman kernel functions'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 January 2023

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Journal articles on the topic "Bergman kernel functions"

1

Mochizuki, Nozomu. "Positive kernel functions and Bergman spaces." Tohoku Mathematical Journal 40, no. 3 (1988): 473–83. http://dx.doi.org/10.2748/tmj/1178227988.

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Jacobson, Robert. "Weighted Bergman kernel functions associated to meromorphic functions." Rocky Mountain Journal of Mathematics 47, no. 1 (2017): 239–57. http://dx.doi.org/10.1216/rmj-2017-47-1-239.

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3

Dong, Robert Xin. "Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves." Complex Manifolds 4, no. 1 (2017): 7–15. http://dx.doi.org/10.1515/coma-2017-0002.

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Abstract We survey variations of the Bergman kernel and their asymptotic behaviors at degeneration. For a Legendre family of elliptic curves, the curvature form of the relative Bergman kernel metric is equal to the Poincaré metric on ℂ \ {0,1}. The cases of other elliptic curves are either the same or trivial. Two proofs depending on elliptic functions’ special properties and Abelian differentials’ Taylor expansions are discussed, respectively. For a holomorphic family of hyperelliptic nodal or cuspidal curves and their Jacobians, we announce our results on the Bergman kernel asymptotics near

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4

Haslinger, Friedrich. "The Bergman kernel functions of certain unbounded domains." Annales Polonici Mathematici 70 (1998): 109–15. http://dx.doi.org/10.4064/ap-70-1-109-115.

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Bekollé, David, and Aline Bonami. "Hausdorff-Young inequalities for functions in Bergman spaces on tube domains." Proceedings of the Edinburgh Mathematical Society 41, no. 3 (1998): 553–66. http://dx.doi.org/10.1017/s001309150001988x.

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We prove that the functions of the Bergman spaces Ap on tube domains may be written as Laplace transforms of functions when 1 ≤ p ≤ 2. We give in this context a generalization of the Hausdorff–Young inequality with the exact constant, and deduce from the case p = 2 the expression of the Bergman kernel as a Laplace transform.

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Herbort, Gregor. "On the invariant differential metrics near pseudoconvex boundary points where the Levi form has corank one." Nagoya Mathematical Journal 130 (June 1993): 25–54. http://dx.doi.org/10.1017/s0027763000004414.

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Let D be a bounded domain in Cn; in the space L2(D) of functions on D which are square-integrable with respect to the Lebesgue measure d2nz the holomorphic functions form a closed subspace H2(D). Therefore there exists a well-defined orthogonal projection PD: L2(D) → H2(D) with an integral kernel KD:D × D → C, the Bergman kernel function of D. An explicit computation of this function directly from the definition is possible only in very few cases, as for instance the unit ball, the complex “ellipsoids” , or the annulus in the plane. Also, there is no hope of getting information about the funct

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7

Bell, Steven R. "Simplicity of the Bergman, Szego and Poisson kernel functions." Mathematical Research Letters 2, no. 3 (1995): 267–77. http://dx.doi.org/10.4310/mrl.1995.v2.n3.a4.

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8

Gergün, Seçil, H. Turgay Kaptanoğlu, and A. Ersin Üreyen. "Harmonic Besov spaces on the ball." International Journal of Mathematics 27, no. 09 (2016): 1650070. http://dx.doi.org/10.1142/s0129167x16500701.

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We initiate a detailed study of two-parameter Besov spaces on the unit ball of [Formula: see text] consisting of harmonic functions whose sufficiently high-order radial derivatives lie in harmonic Bergman spaces. We compute the reproducing kernels of those Besov spaces that are Hilbert spaces. The kernels are weighted infinite sums of zonal harmonics and natural radial fractional derivatives of the Poisson kernel. Estimates of the growth of kernels lead to characterization of integral transformations on Lebesgue classes. The transformations allow us to conclude that the order of the radial der

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Salzo, Saverio, and Johan A. K. Suykens. "Generalized support vector regression: Duality and tensor-kernel representation." Analysis and Applications 18, no. 01 (2019): 149–83. http://dx.doi.org/10.1142/s0219530519410069.

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In this paper, we study the variational problem associated to support vector regression in Banach function spaces. Using the Fenchel–Rockafellar duality theory, we give an explicit formulation of the dual problem as well as of the related optimality conditions. Moreover, we provide a new computational framework for solving the problem which relies on a tensor-kernel representation. This analysis overcomes the typical difficulties connected to learning in Banach spaces. We finally present a large class of tensor-kernels to which our theory fully applies: power series tensor kernels. This type o

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10

Francsics, Gábor, and Nicholas Hanges. "The Bergman Kernel of Complex Ovals and Multivariable Hypergeometric Functions." Journal of Functional Analysis 142, no. 2 (1996): 494–510. http://dx.doi.org/10.1006/jfan.1996.0157.

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Dissertations / Theses on the topic "Bergman kernel functions"

1

Kennell, Lauren R. "Boundary behavior of the Bergman kernel function on strongly pseudoconvex domains with respect to weighted Lebesgue measure." Connect to this title online, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1121801617.

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Thesis (Ph. D.)--Ohio State University, 2005.<br>Title from first page of PDF file. Document formatted into pages; contains vii, 79 p. Includes bibliographical references (p. 79). Available online via OhioLINK's ETD Center

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2

Arroussi, Hicham. "Function and Operator Theory on Large Bergman spaces." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/395175.

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The theory of Bergman spaces has been a central subject of study in complex analysis during the past decades. The book [7] by S. Bergman contains the first systematic treat-ment of the Hilbert space of square integrable analytic functions with respect to Lebesgue area measure on a domain. His approach was based on a reproducing kernel that became known as the Bergman kernel function. When attention was later directed to the spaces AP over the unit disk, it was natural to call them Bergman spaces. As counterparts of Hardy spaces, they presented analogous problems. However, although many problem

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3

Liu, Sheng-Chi. "Mass equidistribution of Hecke eigenforms on the Hilbert modular varieties." Columbus, Ohio : Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1242747349.

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Haimi, Antti. "Polyanalytic Bergman Kernels." Doctoral thesis, KTH, Matematik (Avd.), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-122073.

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The thesis consists of three articles concerning reproducing kernels ofweighted spaces of polyanalytic functions on the complex plane. In the ﬁrst paper, we study spaces of polyanalytic polynomials equipped with a Gaussianweight. In the remaining two papers, more general weight functions are considered. More precisely, we provide two methods to compute asymptotic expansions for the kernels near the diagonal and then apply the techniques to get estimates for reproducing kernels of polyanalytic polynomial spaces equipped with rather general weight functions.<br><p>QC 20130513</p>

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Pokorny, Florian Till. "Bergman kernel on toric Kahler manifolds." Thesis, University of Edinburgh, 2011. http://hdl.handle.net/1842/5301.

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Let (L,h) → (X,ω) be a compact toric polarized Kahler manifold of complex dimension n. For each k ε N, the fibre-wise Hermitian metric hk on Lk induces a natural inner product on the vector space C∞(X,Lk) of smooth global sections of Lk by integration with respect to the volume form ωn /n! . The orthogonal projection Pk : C∞(X,Lk) → H0(X,Lk) onto the space H0(X,Lk) of global holomorphic sections of Lk is represented by an integral kernel Bk which is called the Bergman kernel (with parameter k ε N). The restriction ρk : X → R of the norm of Bk to the diagonal in X × X is called the density func

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Ivarsson, Björn. "Regularity and boundary behavior of solutions to complex Monge–Ampère equations." Doctoral thesis, Uppsala University, Department of Mathematics, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-1603.

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<p>In the theory of holomorphic functions of one complex variable it is often useful to study subharmonic functions. The subharmonic can be described using the Laplace operator. When one studies holomorphic functions of several complex variables one should study the plurisubharmonic functions instead. Here the complex Monge--Ampère operator has a role similar to that of the Laplace operator in the theory of subharmonic functions. The complex Monge--Ampère operator is nonlinear and therefore it is not as well understood as the Laplace operator. We consider two types of boundary value problems f

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7

Klevtsov, Semyon. "Bergman kernel, balanced metrics and black holes." 2009. http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051849.

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Jacobson, Robert Lawrence. "Weighted Bergman Kernel Functions and the Lu Qi-keng Problem." Thesis, 2012. http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11068.

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The classical Lu Qi-keng Conjecture asks whether the Bergman kernel function for every domain is zero free. The answer is no, and several counterexamples exist in the literature. However, the more general Lu Qi-keng Problem, that of determining which domains in Cn have vanishing kernels, remains a difficult open problem in several complex variables. A challenge in studying the Lu Qi-keng Problem is that concrete formulas for kernels are generally difficult or impossible to compute. Our primary focus is on developing methods of computing concrete formulas in order to study the Lu Qi-keng Proble

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9

Lampert, Christoph H. "Der Neumannoperator in streng pseudokonvexen Gebieten mit gewichteter Bergmanmetrik." 2003. http://catalog.hathitrust.org/api/volumes/oclc/52672139.html.

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Miña, Díaz Erwin. "Asymptotics for Faber polynomials and polynomials orthogonal over regions in the complex plane." Diss., 2006. http://etd.library.vanderbilt.edu/ETD-db/available/etd-06062006-132316/.

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Books on the topic "Bergman kernel functions"

1

Boris, Korenblum, and Zhu Kehe 1961-, eds. Theory of Bergman spaces. Springer, 2000.

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2

1964-, Zhang Weiping, and Centre national de la recherche scientifique (France), eds. Bergman kernels and symplectic reduction. Société Mathématique de France, 2008.

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3

Herbort, Gregor. Wachstumsordnung des Bergmankerns auf pseudokonvexen Gebieten. Drucktechnische Zentralstelle der Universität Münster, 1987.

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4

Geometric Analysis of the Bergman Kernel and Metric. Springer, 2013.

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5

Hedenmalm, Hakan, Boris Korenblum, and Kehe Zhu. Theory of Bergman Spaces (Graduate Texts in Mathematics). Springer, 2000.

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6

Ma, Xiaonan, and George Marinescu. Holomorphic Morse Inequalities and Bergman Kernels. Springer London, Limited, 2007.

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7

Holomorphic Morse Inequalities and Bergman Kernels (Progress in Mathematics). Birkhäuser Basel, 2007.

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Book chapters on the topic "Bergman kernel functions"

1

Chang, Der-Chen, Robert Gilbert, and Jingzhi Tie. "Bergman Projection and Weighted Holomorphic Functions." In Reproducing Kernel Spaces and Applications. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8077-0_5.

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2

Khavinson, Dmitry. "[35] (with S. Bergman) Kernel functions and conformal mapping." In Menahem Max Schiffer: Selected Papers Volume 1. Springer New York, 2013. http://dx.doi.org/10.1007/978-0-8176-8085-5_27.

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3

Greene, Robert, and Steven Krantz. "Hilbert spaces of holomorphic functions, the Bergman kernel, and biholomorphic mappings." In Graduate Studies in Mathematics. American Mathematical Society, 2006. http://dx.doi.org/10.1090/gsm/040/14.

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4

Khavinson, Dmitry. "[23] (with S. Bergman) Kernel functions in the theory of partial differential equations of elliptic type." In Menahem Max Schiffer: Selected Papers Volume 1. Springer New York, 2013. http://dx.doi.org/10.1007/978-0-8176-8085-5_22.

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5

Duren, Peter, and Alexander Schuster. "The Bergman kernel function." In Bergman Spaces. American Mathematical Society, 2004. http://dx.doi.org/10.1090/surv/100/02.

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6

Bell, S. "Extendibility of the Bergman kernel function." In Complex Analysis II. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078952.

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7

Arai, Hitoshi. "Bergman-Carleson Measures and Bloch Functions on Strongly Pseudoconvex Domains." In Reproducing Kernels and their Applications. Springer US, 1999. http://dx.doi.org/10.1007/978-1-4757-2987-0_3.

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8

Shapiro, Michael V., and Nikolai L. Vasilevski. "On the Bergmann Kernel Function in the Clifford Analysis." In Clifford Algebras and their Applications in Mathematical Physics. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2006-7_22.

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9

"- The Green’s function and the Bergman kernel." In The Cauchy Transform, Potential Theory and Conformal Mapping. Chapman and Hall/CRC, 2015. http://dx.doi.org/10.1201/b19222-34.

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10

"The Bergman kernel function of some Reinhardt domains." In First International Congress of Chinese Mathematicians. American Mathematical Society, 2001. http://dx.doi.org/10.1090/amsip/020/33.

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Conference papers on the topic "Bergman kernel functions"

1

Fujita, Keiko. "Bergman Kernel for Complex Harmonic Functions on Some Balls." In Proceedings of the 4th International ISAAC Congress. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701732_0039.

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