Functions of Minimal Norm with the Given Set of Fourier Coefficients

Pyotr Ivanshin
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Pyotr Ivanshin: N.I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, 420008 Kazan, Russia

Mathematics, 2019, vol. 7, issue 7, 1-9

Abstract: We prove the existence and uniqueness of the solution of the problem of the minimum norm function ? · ? ∞ with a given set of initial coefficients of the trigonometric Fourier series c j , j = 0 , 1 , … , 2 n . Then, we prove the existence and uniqueness of the solution of the nonnegative function problem with a given set of coefficients of the trigonometric Fourier series c j , j = 1 , … , 2 n for the norm ? · ? 1 .

Keywords: Fourier polynomial; norm; convergence; conditional approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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