INVARIANT SUBSPACES OF ANALYTIC FUNCTIONS. II. SPECTRAL SYNTHESIS OF CONVEX DOMAINS

1972 ◽  
Vol 17 (1) ◽  
pp. 1-29 ◽  
Author(s):  
I F Krasičkov-Ternovskiĭ
Keyword(s):  
Analytic Functions ◽  
Spectral Synthesis ◽  
Invariant Subspaces ◽  
Convex Domains

Invariant subspaces of given index in Banach spaces of analytic functions

1998 ◽  
Vol 1998 (505) ◽  
pp. 23-44 ◽  
Author(s):  
Alexander Borichev
Keyword(s):  
Banach Spaces ◽  
Wide Class ◽  
Analytic Functions ◽  
Unit Disc ◽  
Bergman Spaces ◽  
Invariant Subspaces ◽  
Weighted Bergman Spaces ◽  
Common Zeros ◽  
Spaces Of Analytic Functions

Abstract For a wide class of Banach spaces of analytic functions in the unit disc including all weighted Bergman spaces with radial weights and for weighted ℓAp spaces we construct z-invariant subspaces of index n, 2 ≦ n ≦ + ∞, without common zeros in the unit disc.

scholarly journals Invariant subspaces in Banach spaces of analytic functions.

1990 ◽  
Vol 37 (1) ◽  
pp. 91-104 ◽  
Author(s):  
Håkan Hedenmalm ◽  
Allen Shields
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Invariant Subspaces ◽  
Spaces Of Analytic Functions

The Density of Polynomials in a Special Space of Entire Functions of Exponential Type

2021 ◽  
pp. 34-41
Author(s):  
Aleksandr A. Tatarkin
Keyword(s):  
Exponential Type ◽  
Entire Functions ◽  
Spectral Synthesis ◽  
Traditional Approach ◽  
Complex Domain ◽  
Convex Domains ◽  
Local Description ◽  
Functions Of Exponential Type ◽  
Topological Modules ◽  
Locally Convex

The traditional approach to solving a specific problem of spectral synthesis in a complex domain involves reducing it to the problem of local description of closed submodules in a certain space of entire functions. The last problem is split into checking the stability and saturation of the submodule under study. This approach turned out to be very effective, for example, in the study of submodules of local rank 1 and in the study of submodules in topological modules associated with unbounded convex domains. Recent studies on spectral synthesis in the complex domain are based on a different scheme. This scheme involves reducing the problem of local description to checking the density of polynomials in a special module of entire functions of exponential type. Moreover, the space under study is a separable locally convex space of type (LN)*. Polynomial approximation in such a space is understood by us as sequential approximation, that is, we are talking about the approximation of space elements by ordinary (not generalized) sequences of polynomials. In this article, we study a special locally convex module of entire vector functions over the ring of polynomials in the degree of the independent variable. The theorem proved in the article can serve as a source of new results on spectral synthesis in the complex domain.

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