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Title: Concentration of the L{sub 1}-norm of trigonometric polynomials and entire functions

Abstract

For any sufficiently large n, the minimal measure of a subset of [−π,π] on which some nonzero trigonometric polynomial of order ≤n gains half of the L{sub 1}-norm is shown to be π/(n+1). A similar result for entire functions of exponential type is established. Bibliography: 13 titles.

Authors:
 [1];  [2]
  1. Steklov Mathematical Institute of Russian Academy of Sciences (Russian Federation)
  2. M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22364221
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 205; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CALCULATION METHODS; GAIN; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; POLYNOMIALS

Citation Formats

Malykhin, Yu V, and Ryutin, K S. Concentration of the L{sub 1}-norm of trigonometric polynomials and entire functions. United States: N. p., 2014. Web. doi:10.1070/SM2014V205N11ABEH004431.
Malykhin, Yu V, & Ryutin, K S. Concentration of the L{sub 1}-norm of trigonometric polynomials and entire functions. United States. https://doi.org/10.1070/SM2014V205N11ABEH004431
Malykhin, Yu V, and Ryutin, K S. 2014. "Concentration of the L{sub 1}-norm of trigonometric polynomials and entire functions". United States. https://doi.org/10.1070/SM2014V205N11ABEH004431.
@article{osti_22364221,
title = {Concentration of the L{sub 1}-norm of trigonometric polynomials and entire functions},
author = {Malykhin, Yu V and Ryutin, K S},
abstractNote = {For any sufficiently large n, the minimal measure of a subset of [−π,π] on which some nonzero trigonometric polynomial of order ≤n gains half of the L{sub 1}-norm is shown to be π/(n+1). A similar result for entire functions of exponential type is established. Bibliography: 13 titles.},
doi = {10.1070/SM2014V205N11ABEH004431},
url = {https://www.osti.gov/biblio/22364221}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 11,
volume = 205,
place = {United States},
year = {Sun Nov 30 00:00:00 EST 2014},
month = {Sun Nov 30 00:00:00 EST 2014}
}