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Mat. Zametki, 2011, Volume 89, Issue 6, Pages 894–913 (Mi mz8543)  

This article is cited in 1 scientific paper (total in 1 paper)

Bases of Exponentials in Weighted Spaces Generated by Zeros of Functions of Sine Type

A. M. Sedletskii

M. V. Lomonosov Moscow State University

Abstract: If $\omega$ is an $A_p$-weight with some additional condition and $(\lambda)$ is a separated sequence of all zeros of a sine-type function possessing a certain multiplier (in the sense of Fourier transforms) property, then the corresponding system of exponentials $(e^{i\lambda_nt})$ constitutes a basis in the weighted space $L^p((-\pi,\pi),\omega(t) dt)$, $1<\pi<\infty$.

Keywords: basis of exponentials, weighted space, sine-type function, $A_p$-weight, Riesz property, Fourier multiplier, weighted multiplier, Laplace transformation, Hölder's inequality

DOI: https://doi.org/10.4213/mzm8543

Full text: PDF file (617 kB)
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English version:
Mathematical Notes, 2011, 89:6, 853–870

Bibliographic databases:

UDC: 517.982.25
Received: 03.06.2009
Revised: 01.02.2010

Citation: A. M. Sedletskii, “Bases of Exponentials in Weighted Spaces Generated by Zeros of Functions of Sine Type”, Mat. Zametki, 89:6 (2011), 894–913; Math. Notes, 89:6 (2011), 853–870

Citation in format AMSBIB
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\paper Bases of Exponentials in Weighted Spaces Generated by Zeros of Functions of Sine Type
\jour Mat. Zametki
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\jour Math. Notes
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    This publication is cited in the following articles:
    1. S. S. Pukhov, “Bases of Exponentials in Weighted Spaces Generated by Zeros of the Fourier–Stieltjes Transform”, Math. Notes, 95:6 (2014), 820–832  mathnet  crossref  crossref  mathscinet  isi  elib
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