An Explicit Formula for Minimal Interpolation in Hardy Spaces

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Date
2022
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Publisher
University of Alabama Libraries
Abstract

We will look at minimal interpolation problems in the Hardy space H2 using a linear algebra approach. The problem we investigate is to find the function of smallest norm with specified values at given points. We consider the kernel matrix. We find an explicit determinant for a generalized version of this matrix. Then we find an inverse matrix for the kernel matrix. We will use our result about inverse matrices to give a different proof of the main interpolation theorem for Hardy spaces.

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Electronic Thesis or Dissertation
Keywords
Analysis, Bergman Spaces, Complex Analysis, Functional Analysis, Hardy Spaces, Operator Theory
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