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  • 1 I. Javakhishvili Tbilisi State University, 2, University St., Tbilisi 0128, Georgia
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Abstract

Properties of Fourier–Haar coefficients of continuous functions are studied. It is established that Fourier–Haar coefficients of continuous functions are monotonic in a certain sense for convex functions. Questions of quasivariation of Fourier–Haar coefficients of continuous functions are also considered.

  • [1] Alexits, G. 1961 Convergence Problems of Orthogonal Series International Series of Monographs in Pure and Applied Mathematics 20 Pergamon Press New York–Oxford–Paris translated from German.

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  • [2] Golubov, B. I. 1964 On Fourier series of continuous functions with respect to a Haar system Izv. Akad. Nauk SSSR Ser. Mat. 28 12711296 in Russian.

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  • [3] Tsagareishvili, V. Sh. 2004 On the variation of the Fourier–Haar coefficients Mat. Sb. 195 143160 translation in Sb. Math., 195 (2004), 441–457 (in Russian).

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  • [4] Tsagareishvili, V. Sh. 1971 The Fourier coefficients of a continuous function with respect to the Haar system Soobshch. Akad. Nauk Grusin. SSR (Bull. Georgian Acad. Sci.) 63 3739 (in Russian).

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  • [5] Timan, A. F. 1960 Theory of Approximation of Functions of a Real Variable Gosudarstv. Izdat. Fiz.-Mat. Lit. Moscow in Russian.

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