Affordable Access

Access to the full text

Representing Systems of Exponentials in Projective Limits of Weighted Subspaces of A∞(D)

Authors
  • Isaev, K. P.1, 2
  • 1 Institute of Mathematics with Computer Center of the Ufa Science Center of the Russian Academy of Sciences, ul. Chernyshevskogo 112, Ufa, 450008, Russia , Ufa (Russia)
  • 2 Bashkirian State University, ul. Z. Validi 23, Ufa, 450074, Russia , Ufa (Russia)
Type
Published Article
Journal
Russian Mathematics
Publisher
Pleiades Publishing
Publication Date
Jan 01, 2019
Volume
63
Issue
1
Pages
24–34
Identifiers
DOI: 10.3103/S1066369X19010031
Source
Springer Nature
Keywords
License
Yellow

Abstract

We introduce a normed space of functions, holomorphic in a bounded convex domain. Its elements are infinitely differentiable up to the boundary, and all their derivatives satisfy estimates specified by a convex sequence of positive numbers. We consider its largest linear subspace that is invariant with respect to the operator of differentiation and provide it with the natural topology of projective limit. We establish duality between this subspace and some space of entire functions. Based on this, we construct a representing system of exponentials in the subspace.

Report this publication

Statistics

Seen <100 times