On the optimal analytic continuation from discrete data

Narek Hovsepyan

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arXiv · 2106.01471

On the optimal analytic continuation from discrete data

Narek Hovsepyan

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Abstract

We consider analytic functions from a reproducing kernel Hilbert space. Given that such a function is of order $\epsilon$ on a set of discrete data points, relative to its global size, we ask how large can it be at a fixed point outside of the data set. We obtain optimal bounds on this error of analytic continuation and describe its asymptotic behavior in $\epsilon$. We also describe the maximizer function attaining the optimal error in terms of the resolvent of a positive semidefinite, self-adjoint and finite rank operator.

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Narek Hovsepyan. 2021-06-02. On the optimal analytic continuation from discrete data. https://arxiv.org/abs/2106.01471

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