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Showing 1 to 8 of 8 for “"Bergman Projection"”.
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Regularity of the Bergman Projection on Variants of the Hartogs Triangle
The Bergman projection is the orthogonal projection from the space of square integrable functions onto the space of square integrable holomorphic functions on a domain. Initially, the projection is defined on the L2 space, but its behavior on other function spaces, e.g. Lp, Sobolev and Holder …
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Regularity of the D-bar-Neumann Operator, the Bergman Projection and the Canonical Solution Operator of D-bar-Equation
… operator, the canonical solution operator, the Bergman projection and the Hankel operator. Meanwhile, the study of these operators is deeply related to the regularity of the $\bar{\partial}$-problem. In this thesis, we focus on the regularity, compactness and boundedness of these operators.</p> …
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Diederich-Fornæss Index on Boundaries Containing Crescents
… that fails to satisfy global regularity of the Bergman Projection, due to the set of weakly pseudoconvex points that form an annulus in its boundary. We instead examine a bounded pseudoconvex domain Ω ⊂ C2 whose set of weakly pseudoconvex points form a crescent in its boundary. In 2019, …
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Hartogs Domains and the Diederich-Fornæss Index
… a crucial role in studying regularity of the Bergman projection on pseudoconvex domains in Sobolov spaces as is shown by Kohn, Harrington, Pinton and Zampieri and others. In this work, we discuss the Diederich-Fornss Index on Hartogs domains, and its relation to other properties connected to …
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Operators on some analytic function spaces and their dyadic counterparts
… problem on the bitorus, boundedness of the Bergman projection and analytic Besov spaces in tube domains over symmetric cones. In part I of this thesis, we show how to generate Carleson measures from a class of weighted Carleson measures in the unit ball. The results are used to obtain …
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The Szego Kernel for Non-Pseudoconvex Domains in C<sup>2</sup>
… boundary ∂Ω. There are two closely related projections that are of particular interest. The <em>Bergman projection</em> <strong><em>B</em></strong> is the orthogonal projection of L<sup>2</sup>(Ω) onto the closed subspace L<sup>2</sup>(Ω)∩O(Ω), where O(Ω)is the space of all holomorphic …
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The Szego Kernel for Non-Pseudoconvex Domains in C<sup>2</sup>
… boundary ∂Ω. There are two closely related projections that are of particular interest. The <em>Bergman projection</em> <strong><em>B</em></strong> is the orthogonal projection of L<sup>2</sup>(Ω) onto the closed subspace L<sup>2</sup>(Ω)∩O(Ω), where O(Ω)is the space of all holomorphic …
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A new computation of the Bergman kernel and related techniques
We introduce a technique for obtaining the Bergman kernel on certain Hartogs domains. To do so, we apply a differential operator to a known kernel function on a domain in lower dimensional space. We rediscover some known results and we obtain new explicit formulas. Using these formulas, we analyze …