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Convergence and Integrability of Series with Monotone Decreasing Coefficients by Chrestenson-Levy Systems


Affiliations
1 State Engineering University of Armenia, Yerevan, Teryan st.105, 375049, Armenia
     

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In this paper we consider problems of convergence and integrability of series with monotone decreasing coefficients by Chrestenson - Levy systems. In particular we generalize some results, known for classical Walsh systems. Interest in questions arises due to a rapidly developed greedy algorithm in recent years, where in particular the important role played a representation of functions by series with monotone coefficients.

Keywords

Chrestenson-Levy Systems, Monotonic Coeffcients, Convergence, Integrability.
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  • H.E. Chrestenson, A class of generalized Walsh functions, Pacific J. Math., 45 (1955), 17-31.

  • P. Levy, Sur une generalisation des fonotions orthogonales de Rademacher, Comment. math. helv., 16 (1944), 146-152.

  • R.E. A.C. Paley, A remarkable set of orthogonal functions, Proc. London Math. Soc., 34 (1932), 241-279.

  • J. Fine, The generalized Walsh functions, Trans. Amer. Math. Soc., 69 (1950), 66-77.

  • C. Watari, On generalized Walsh-Fourier series, Proc. Japan Acad., 33 (1957), 435-438.

  • N. Vilenkin, On a class of complete orthonormal systems, Izv. Math. 28 (1963), 1-35.

  • W. Young, Mean convergence of generalized Walsh - Fourier series, Trans. Amer. Math.Soc., 218 (1976), 311-320.

  • Yano S. On Walsh Fourier series, TShoku Math. Jour., 3 (1951), 223-242.

  • S.A. Episkoposian, On greedy algorithms with respect to generalized Walsh system, GJPAM, 3 (2007), 77-86.

  • Kaczmarcz S., Steinhaus G., Theory of Orthogonal Series, Moscow, 1958.

  • B.I. Golubov, A. Emov, V. Skvortsov, Walsh Series and Transforms. Kluwer Academic Publishers, Dordrecht, 1991.

  • Shneider A.A., On series with respect to Walsh functions with monotone coefficients, Izv. Akad. Nauk SSSR, Ser. Mat., 12 (1948), 179-192.

  • Rubenstein A.I., The A - integral and series in the Walsh system, Uspekhi Mat. Nauk, 18 (1963), 191-197.

  • Balashov L.A., On series with respect to a Walsh system with monotone coecients, Sib. Math. J., 12 (1970), 25-39,

  • Olevskii A.M., Order growth of the Lebesque functions of bounded orthonormal systems, Dokl. Akad. Nauk SSSR, 176 (1967), 1247-1250.


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  • Convergence and Integrability of Series with Monotone Decreasing Coefficients by Chrestenson-Levy Systems

Abstract Views: 314  |  PDF Views: 1

Authors

S. A. Episkoposian
State Engineering University of Armenia, Yerevan, Teryan st.105, 375049, Armenia
T. M. Saghatelyan
State Engineering University of Armenia, Yerevan, Teryan st.105, 375049, Armenia

Abstract


In this paper we consider problems of convergence and integrability of series with monotone decreasing coefficients by Chrestenson - Levy systems. In particular we generalize some results, known for classical Walsh systems. Interest in questions arises due to a rapidly developed greedy algorithm in recent years, where in particular the important role played a representation of functions by series with monotone coefficients.

Keywords


Chrestenson-Levy Systems, Monotonic Coeffcients, Convergence, Integrability.

References