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1	Two problems in the theory of Toeplitz operators on the Bergman space / Yousef, Abdelrahman F. January 2009 (has links) Dissertation (Ph.D.)--University of Toledo, 2009. / Typescript. "Submitted as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Mathematics." Bibliography: leaves 57-59. Bergman spaces. Toeplitz operators.
2	Putnam's Inequality and Analytic Content in the Bergman Space Fleeman, Matthew 16 June 2016 (has links) In this dissertation we are interested in studying two extremal problems in the Bergman space. The topics are divided into three chapters. In Chapter 2, we study Putnam’s inequality in the Bergman space setting. In [32], the authors showed that Putnam’s inequality for the norm of self-commutators can be improved by a factor of 1 for Toeplitz operators with analytic symbol φ acting on the Bergman space A2(Ω). This improved upper bound is sharp when φ(Ω) is a disk. We show that disks are the only domains for which the upper bound is attained. In Chapter 3, we consider the problem of finding the best approximation to z ̄ in the Bergman space A2(Ω). We show that this best approximation is the derivative of the solution to the Dirichlet problem on ∂Ω with data \|z\|2 and give examples of domains where the best approximation is a polynomial, or a rational function. Finally, in Chapter 4 we study Bergman analytic content, which measures the L2(Ω)-distance between z ̄ and the Bergman space A2(Ω). We compute the Bergman analytic content of simply connected quadrature domains with quadrature formula supported at one point, and we also determine the function f ∈ A2(Ω) that best approximates z ̄. We show that, for simply connected domains, the square of Bergman analytic content is equal to torsional rigidity from classical elasticity theory, while for multiply connected domains these two domain constants are not equivalent in general. Bergman spaces Operator theory Approximation theory Mathematics
3	Bergman space methods and integral means spectra of univalent functions Sola, Alan January 2007 (has links) We study universal integral means spectra of certain classes of univalent functions defined on subsets of the complex plane. After reformulating the definition of the integral means spectrum of a univalent function in terms of membership in weighted Bergman spaces, we describe the Hilbert space techniques that can be used to estimate universal means spectra from above. Finally, we show that the method of norm expansion used in that context can be applied in a more general setting to reproducing kernel spaces in order to explicitly compute kernel functions. / <p>QC 20101117</p> Univalent functions integral means spectra Bergman spaces Mathematics Matematik
4	Bergman space methods and integral means spectra of univalent functions Sola, Alan January 2007 (has links) <p>We study universal integral means spectra of certain classes of univalent functions defined on subsets of the complex plane. After reformulating the definition of the integral means spectrum of a univalent function in terms of membership in weighted Bergman spaces, we describe the Hilbert space techniques that can be used to estimate universal means spectra from above. Finally, we show that the method of norm expansion used in that context can be applied in a more general setting to reproducing kernel spaces in order to explicitly compute kernel functions.</p> Univalent functions integral means spectra Bergman spaces Algebra, geometri och analys
5	The analysis of Toeplitz operators, commutative Toeplitz algebras and applications to heat kernel constructions. / The analysis of Toeplitz operators, commutative Toeplitz algebras and applications to heat kernel constructions. Issa, Hassan 19 June 2012 (has links) No description available. 510 Mathematik EDCA 360 EDCA 350 EDAD 550 EDA 020 ECI 020 ECI 990 ECIA 150 EDA 020 EDAD 150 EDCA 700 EEE 010 EEGJ 990 EEHF 050 Mathematics and Computer Science Bergman Räumen Toeplitz Operatoren Kommutativer Algebren Wärmeleitungskerne sub-ellipttischer operatoren Kompakt Toeplitz operatoren Berezin transformation beschränkten symmetrichen Gebieten Bergman spaces Toeplitz operators commutative algebras heat kernel construction sub-elliptic Operators Compact Toeplitz Operators Berezin transform Bounded symmetric domains 31.47 31.46 31.45 31.41 31.42 31.43 31.55

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