A Hilbert space approach to singularities of functions
| Autor: | Agler, Jim, Lykova, Zinaida, Young, N. J. |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 52 pages. This version includes minor revisions. The paper has been accepted for publication by the Journal of Functional Analysis |
| Databáze: | arXiv |
| Externí odkaz: |
|