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Том 241, № 6 (2019)
- Год: 2019
- Статей: 10
- URL: https://ogarev-online.ru/1072-3374/issue/view/15025
Article
Classical Operators in Weighted Banach Spaces of Holomorphic Functions
Аннотация
We review recent results in the theory of classical operators (embedding, differentiation, and integration) in weighted Banach spaces of holomorphic functions with uniform estimates. We formulate and analyze results based on associated and essential weights.
647-657
Principal Submodules in the Module of Entire Functions, Which is Dual to the Schwarz Space, and Weak Spectral Synthesis in the Schwartz Space
Аннотация
We obtain a sufficient condition of the weak localizability of a principal submodule in the module of entire functions of exponential type and polynomial growth on the real line. Applications to the problem of the (weak) spectral synthesis in the Schwartz space C∞ (a; b) are discussed.
658-671
672-685
The Order of the Dirichlet Series in the Half-Strip
Аннотация
We study the Dirichlet series whose domain of convergence is the half-plane, and the sequence of exponents can be extended to a certain “regular” sequence. We prove that the k-orders of the Dirichlet series are the same in all the half-strips whose widths are greater than a certain number called the special density of the distribution of exponents.
686-700
Quasianalytic Functional Classes in Jordan Domains of the Complex Plane
Аннотация
In this paper, we study the Carleman classes in Jordan domains of the complex plane. We obtain a quasianalyticity criterion for the regular Carleman classes, which is universal for all weakly uniform domains. The proof is based on the solution of the Dirichlet problem with an unbounded boundary function and a Beurling result on the estimate of the harmonic measure.
701-717
Generating Functions for Bases in Hilbert Spaces of Entire Functions
Аннотация
We prove that unconditional bases in a functional Hilbert space H have a generating function if and only if the space H is stable. Necessary and sufficient conditions for the stability of spaces adjoint to weighted spaces on an interval are obtained.
718-726
727-734
Sketch of the Theory of Growth of Holomorphic Functions in a Multidimensional Torus
Аннотация
We develop an approach to the theory of growth of the class H(????n) of holomorphic functions in a multidimensional torus ????n based on the structure of elements of this class and well-known results of the heory of growth of entire functions of several complex variables. This approach is illustrated in the case where the growth of the function g ∈ H(????n) is compared with the growth of its maximum modulus on the skeleton of the polydisk. The properties of the corresponding characteristics of growth of the functions in the class H(????n) are studied with their relation to coefficients of the corresponding Laurent series. A comparative analysis of these results and similar assertions of the theory of growth of entire functions of several variables is given.
735-749
Metric Spaces of Bounded Analytical Functions
Аннотация
In this paper, we consider classes of analytical functions that map the unit disk into itself. Functions of these classes can be described in terms of hyperbolic derivative and hyperbolic metric. Under an appropriate choice of the corresponding metrics, these classes are metric spaces. Functions of the hyperbolic classes considered generate composition operators from the Bloch space into classical spaces of analytical functions in the unit disk.
750-759
On Invariant Subspaces of the Pommiez Operator in the Spaces of Entire Functions of Exponential Type
Аннотация
We describe closed invariant eigenspaces of the Pommmiez operator in the (LF)-space of entire functions of exponential type. This space is topologically equivalent (by means of the Laplace transform) to the strong dual space of all germs of functions that are analytic on a convex, locally closed subset of the complex plane.
760-769