Uniqueness of series with respect to general Franklin systems

Journal of Contemporary Mathematical Analysis - Tập 44 Số 5 - Trang 271-283 - 2009
G. G. Gevorkyan1, Anna Kamont2
1Yerevan State Univ.
2Institute of Mathematics, Polish Academy of Sciences, Sopot, Poland

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Tài liệu tham khảo

F. G. Arutunyan, A. A. Talalian, “Uniquness of Series in Haar and Walsh Systems” (in Russian). Izv. Akad. Nauk SSSR, Ser. Mat., 28, 1391–1408 (1964).

Z. Ciesielski, Orthogonal Projections onto Spline Spaces with Arbitrary Knots, in: Function spaces (Pozna’n 1998), Lecture Notes in Pure and Appl. Math., 213, 133–140 (Dekker, New York, 2000).

Z. Ciesielski, J. Domsta, “Estimates for the Spline Orthonormal Functions and for their Derivatives”, Studia Math., 44, 315–320 (1972).

Z. Ciesielski, A. Kamont, “Projections onto Piecewise Linear Functions”, Funct. Approx. Comment. Math., 25, 129–143 (1997).

I. Daubechies, “Orthonormal Bases of Compactly Supported Wavelets”, Comm. Pure Appl. Math., 41(7), 909–996, (1988).

G. G. Gevorkyan, “Series in the Franklin System” (in Russian), Erevan Gos. Univ. Uchen. Zap. Estestv. Nauk, no. 2(162), 146–148 (1986).

G. G. Gevorkyan, “Uniquness of Series in the Franklin System” (in Russian), Mat. Zametki, 46(2), 51–58 (1989).

G. G. Gevorkyan, “Some Problems on Franklin Series”, Izv. NAN Armenii, Matematika [Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)] 39(2), 77–81 (2004).

G. G. Gevorkyan, “Ciesielski and Franklin Systems”, in: Approximation and Probability, (85–92), Banach Center Publ., 72 (Polish Acad. Sci., Warsaw, 2006).

G. G. Gevorkyan, A. Kamont, “On General Franklin Systems”, Dissertationes Mathematicae (Rozprawy Matematyczne) 374, 1–59 (1998).

A. Kamont, “Characterization of Hölder Spaces Corresponding to Ditzian-Totik Modulus of Smoothness”, Approx. Theory and its Applications, 16, 73–91, (2000).

Y. Meyer, “Ondelettes sur L’intervalle”, Rev. Mat. Iberoamericana, 7(2), 115–133, (1991).

J. - O. Strömberg, “AModified Franklin System and Higher Order Spline Systems on R n as Unconditional Bases for Hardy Spaces”, in: Conf. in Honor of A. Zygmund, vol. II, 475–493 (W. Beckner et all. ed., Wadsworth Math. Series, 1983).