Date: Monday, October 23, 2017
Location: 3096 East Hall (4:00 PM to 5:00 PM)
Title: Constructing holomorphic L^p functions from L^p data
Abstract: For a domain U in C^n, let A^p(U) denote the subset of functions belonging to L^p(U) that are holomorphic. Given a map f in L^p(U), can we use it to construct a "natural" function in A^p(U)? The Bergman kernel is a useful tool that can be used to investigate this question, but there are certain limitations. I will show that Hilbert space methods may still be employed to attack this problem, even when the Bergman kernel fails to do the job. I plan to focus on a class of model domains and introduce new family of integral kernels which avoid the issues that limit the Bergman kernel. This work is joint with Debraj Chakrabarti and Jeff McNeal.
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Speaker: Luke Edholm
Institution: U(M)
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