|
This article is cited in 3 scientific papers (total in 3 papers)
Multiplication operators in spaces of entire functions of finite order and operators of convolution type
O. V. Epifanov
Abstract:
This article deals with the operator $L_a$ of multiplication by an entire function $a(z)$ with indicator $h(\theta)$ when the order is $\rho$. This operator acts from $[\rho,\mathscr K)$ to $[\rho,\mathscr K+h)$, where $\mathscr K$ is a sequence of indicators, $[\rho,\mathscr K)=\operatorname{span}\bigcup_{k\in\mathscr K}[\rho,k]=\lim_{k\in\mathscr K}\operatorname{ind}[\rho,k]$, with $[\rho,k]$ the standard space of entire functions. It is assumed that the spaces are isomorphic, with respect to a transformation of Borel type, to spaces of functions analytic on many-sheeted closed sets. A criterion is found for the range of $L_a$ to be closed. It is used to derive, in particular, a criterion for an operator of convolution type in a union of $\rho$-convex domains to be an epimorphism, along with known results about convolution operators and operators of convolution type. The conditions connect the directions of non-completely-regular growth of $a(z)$ and of accumulation of its zeros with geometric characteristics of $\mathscr K$.
Bibliography: 26 titles.
Received: 15.04.1982
Citation:
O. V. Epifanov, “Multiplication operators in spaces of entire functions of finite order and operators of convolution type”, Mat. Sb. (N.S.), 120(162):4 (1983), 505–527; Math. USSR-Sb., 48:2 (1984), 499–520
Linking options:
https://www.mathnet.ru/eng/sm2144https://doi.org/10.1070/SM1984v048n02ABEH002688 https://www.mathnet.ru/eng/sm/v162/i4/p505
|
Statistics & downloads: |
Abstract page: | 380 | Russian version PDF: | 139 | English version PDF: | 13 | References: | 54 |
|