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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2001, Volume 232, Pages 94–101 (Mi tm206)  
This article is cited in 6 scientific papers (total in 6 papers)

A Method for Estimating the $L_1$ Norm of an Exponential Sum Based on Arithmetic Properties of the Spectrum

S. V. Bochkarev
Full-text PDF (155 kB) Citations (6)
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Abstract: A new lower estimate of the $L_1$ norm of a general exponential sum is established in terms of the ratios of the $L_p$ ($p>2$) and $L_2$ norms of dyadic blocks. In particular, for sums of exponents with coefficients whose absolute values are 0 and 1, the estimates are found such that the density and arithmetic properties of the spectrum are simultaneously taken into account. The results obtained are unimprovable in a certain sense.
Received in October 2000
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: S. V. Bochkarev, “A Method for Estimating the $L_1$ Norm of an Exponential Sum Based on Arithmetic Properties of the Spectrum”, Function spaces, harmonic analysis, and differential equations, Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 232, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 94–101; Proc. Steklov Inst. Math., 232 (2001), 88–95
Citation in format AMSBIB
\Bibitem{Boc01}
\by S.~V.~Bochkarev
\paper A~Method for Estimating the $L_1$ Norm of an Exponential Sum Based on Arithmetic Properties of the Spectrum
\inbook Function spaces, harmonic analysis, and differential equations
\bookinfo Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2001
\vol 232
\pages 94--101
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm206}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1851442}
\zmath{https://zbmath.org/?q=an:1007.42002}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 232
\pages 88--95
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    • This publication is cited in the following 6 articles:
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