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Functions of Minimal Norm with the Given Set of Fourier Coefficients

Author

Listed:
  • Pyotr Ivanshin

    (N.I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, 420008 Kazan, Russia)

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 .

Suggested Citation

  • Pyotr Ivanshin, 2019. "Functions of Minimal Norm with the Given Set of Fourier Coefficients," Mathematics, MDPI, vol. 7(7), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:651-:d:250253
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    References listed on IDEAS

    as
    1. Pyotr N. Ivanshin, 2015. "Conditional Optimization and One Inverse Boundary Value Problem," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, July.
    2. Dette, Holger & Melas, Viatcheslav B., 2005. "A note on some extremal problems for trigonometric polynomials," Technical Reports 2005,20, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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