Functions of minimal norm with the given set of Fourier coefficients

Abstract

© 2019 by the authors. 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 cj, j = 0, 1, . . ., 2n. 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 cj, j = 1, . . ., 2n for the norm ∥ . ∥1.