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arXiv · 2205.05012

A Hilbert space approach to singularities of functions

Jim Agler·Zinaida Lykova·N. J. Young
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Abstract

We introduce the notion of a pseudomultiplier of a Hilbert space $\mathcal H$ of functions on a set $\Omega$. Roughly, a pseudomultiplier of $\mathcal H$ is a function which multiplies a finite-codimensional subspace of $\mathcal H$ into $\mathcal H$, where we allow the possibility that a pseudomultiplier is not defined on all of $\Omega$. A pseudomultiplier of $\mathcal H$ has singularities, which comprise a subspace of $\mathcal H$, and generalize the concept of singularities of an analytic function, even though the elements of $\mathcal H$ need not enjoy any sort of analyticity. We analyse the natures of these singularities, and obtain a broad classification of them in function-theoretic terms.

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BibTeXRIS

Jim Agler, Zinaida Lykova, N. J. Young. 2022-05-10. A Hilbert space approach to singularities of functions. https://arxiv.org/abs/2205.05012

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