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:
-
- Steklov Mathematical Institute of Russian Academy of Sciences (Russian Federation)
- 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}
}
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