Abstract
We obtain the criterion of solvability of homogeneous convolution equation in a half-strip. Proof is based on a new decomposition property of the weighted Hardy space. This result has relations to the spectral analysis-synthesis problem, cyclicity problem, information theory. All data generated or analysed during this study are included in this published article.
Highlights
Convolution operations are very important in mathematical community, as well as in signal processing, sampling, filter design and applications
The aim of this paper is to obtain an equivalent result to Theorem 1.1 for the convolution equation on half-strip
Sedletskii [17] proved that the space H p(C+) can be defined as the class of analytic on C+ functions for which
Summary
Convolution operations are very important in mathematical community, as well as in signal processing, sampling, filter design and applications. Lax et al (see [1]–[3]) considered the equation f (u + τ )g(u)du = 0, τ ≤ 0, g ∈ L2(−∞; 0),. This article is part of the topical collection “Harmonic Analysis and Operator Theory” edited by H.
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