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The Bergman kernel of fat Hartogs triangles

Edholm, Luke David
http://rave.ohiolink.edu/etdc/view?acc_num=osu1466474083

Abstract Details

2016, Doctor of Philosophy, Ohio State University, Mathematics.
My research is concerned with Bergman theory, both as a tool to answer deep questions in Several Complex Variables, and an object of study in its own right. Much of my research has involved an infinite family of domains in C^2 which I call generalized Hartogs triangles. These are bounded, pseudoconvex domains with a specific type of boundary singularity generalizing the classical Hartogs triangle. The boundaries of these domains are responsible for new function theoretic behavior. I compute a closed form expression for the Bergman kernel for all generalized Hartogs triangles with a rational exponent gamma. In each case, the kernel is given by an explicit rational function. Underlying this computation is the observation that the Bergman space admits an essential decomposition into a finite number of subspaces. With this decomposition, I am able to study the action of the Bergman projection on L^p-spaces associated to these domains. When gamma is rational, there is a restricted non-trivial interval of p values for which the Bergman projection is a bounded operator on L^p. However, when gamma is irrational, the Bergman projection is shown to be bounded if and only if p=2.
Jeffery McNeal (Advisor)
Kenneth Koenig (Committee Member)
Christopher Miller (Committee Member)
102 p.
Mathematics
Bergman theory, complex analysis

Recommended Citations

Citations

  • Edholm, L. D. (2016). The Bergman kernel of fat Hartogs triangles [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1466474083

    APA Style (7th edition)

  • Edholm, Luke. The Bergman kernel of fat Hartogs triangles. 2016. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1466474083.

    MLA Style (8th edition)

  • Edholm, Luke. "The Bergman kernel of fat Hartogs triangles." Doctoral dissertation, Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1466474083

    Chicago Manual of Style (17th edition)

osu1466474083
997
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This open access ETD is published by The Ohio State University and OhioLINK.