Equivalent definition of some weighted Hardy spaces

Dilnyi, Volodymyr

doi:10.1007/s11253-009-0140-1

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Cited by 3 publications

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“…The main result. The decomposition problem for functions in Paley-Wiener space W 1 σ into the sum of two functions each of them characterized by the module which is "big" only in the upper or lower half-planes was investigated by B. V. Vynnytskyi and his followers (see [7], [8]). R. S. Yulmukhametov in [9] solved the problem of decomposition (splitting) into the product of two functions for some subspace of the Paley-Wiener space.…”

Section: Definitionmentioning

confidence: 99%

Hilbert transform on $W_{\sigma}^1$

Dilnyi

Voitovych

2019

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Section: Definitionmentioning

confidence: 99%

Hilbert transform on $W_{\sigma}^1$

Dilnyi

Voitovych

2019

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Solvability Criterion for Convolution Equations on a Half-Strip

Dilnyi

2021

Complex Anal. Oper. Theory

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On the Decomposition Problem for Functions of Small Exponential Type

Voitovych

2023

BMJ

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The technique of decomposition for functions into the sum or product of two functions is often used to facilitate the study of properties of functions. Some decomposition problems in the weighted Hardy space, Paley-Wiener space, and Bergman space are well known. Usually, in these spaces, functions are represented as the sum of two functions, each of them is "big" only in the first or only in the second quarter. The problem of decomposition of functions has practical applications, particularly in information theory. In these applications, it is often necessary to find those solutions of the decomposition problem whose growth on the negative real semi-axis is "small". In this article we consider the decomposition problem for an entire function of any small exponential type in $\{z:\Re z<0\}$. We obtain conditions for the existence of solutions of the above problem.

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Equivalent definition of some weighted Hardy spaces

Cited by 3 publications

References 5 publications

Hilbert transform on $W_{\sigma}^1$

Hilbert transform on $W_{\sigma}^1$

Solvability Criterion for Convolution Equations on a Half-Strip

On the Decomposition Problem for Functions of Small Exponential Type

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