Frame Properties of a Part of the System of Exponents in Hardy Weighted Classes

Togrul R. Muradov^1,

¹Department of nonharmonic analysis, Institute of Mathematics and Mechanics, National Academy of Sciences, Baku, Azerbaijan

Cite this paper:
Togrul R. Muradov. Frame Properties of a Part of the System of Exponents in Hardy Weighted Classes. American Journal of Mathematical Analysis. 2013; 1(1):1-7. doi: 10.12691/ajma-1-1-1

Abstract

We consider a part of the classic system of exponents, study its frame property in Hardy weighted classes when, generally speaking the weight may not satisfy the Muckenhoupt condition.

Keywords:
system of exponents Hardy weighted class

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References:

[1]	Zigmund A. Trigonometric series, 1, Mir, Moscow, 1965, 616.
[2]	Zigmund A. Trigonometric series, 2, Mir, Moscow, 1965, 538.
[3]	Edwards R. Fourier series in modern statement. 1, Mir, Moscow, 1985, 264.
[4]	Edwards R. Fourier series in modern statement. 2, Mir, Moscow, 1985, 400.
[5]	Bari N.K. Trigonometric series, Fzimatgiz, Moscow, 1961, 672.
[6]	Babenko K.I. On conjugated functions. DAN SSSR, 62(2), 1948, 157-160.
[7]	Gaposhkin V.F. On a generalization of M.Riesz theorem on conjugated functions. Mat. sbornik, 46 (88), 3 , 1958, 111-115.
[8]	Kazaryan K.S., Lizorkin P.I. Multipliers, bases and unconditional bases in the weighted spaces B and SB, Proc. of the Steklov Ins. of Math., 187, 1989, 111-130.
[9]	Garnett S. Bounded analytic functions. Mir, Moscow, 1984, 469.
[10]	Moiseev E.I. On basicity of the system of sines and cosines in weighted space. Diff. uravn., 34(1), 1998, 40-44.
[11]	Moiseev E.I. Basicity in weighted space of a system of eigen functions of differential operator. Diff. uravn, 35(2), 1999, 200-205.
[12]	Pukhov S.S., Sedletsky A.M. Bases of exponents sines and cosines in weighted spaces on a finite interval. Dokl. RAN, 425(4), 2009, 452-455.
[13]	Bilalov B.T., Veliyev S.G. On completeness of exponent system with complex coefficients in weight spaces. Trans. Of NAS of Az., XXV(7), 2005, 9-14.
[14]	Bilalov B.T., Veliyev S.G. Bases of eigen functions of two discontinuous differential operators. Diff. uravn., 42(9), 2006, 190-192.
[15]	Golubeva E.G. Frames of exponents with power weight. Vestnik Sam. State Univer., 2(83), 2011, 15-25.
[16]	Bilalov B.T., Guliyeva F.A. On The Frame Properties of Degenerate System of Sines. Journal of Function Spaces and Applications, v. 2012 (2012).
[17]	Mamedova Z.V. On basis properties of degenerate exponential system. Applied Mathematics, 3(12), December 2012.
[18]	Heil Ch. A Basis Theory Primer, Springer, 2011, 534.
[19]	Christensen O. An Introduction to Frames and Riesz bases. Springer, 2003, 440.
[20]	Rahimi A. Frames and Their Generalizations in Hilbert and Banach Spaces, Lambert Academic Publishing, 2011, 136.
[21]	Singer I. Bases in Banach spaces, I, AP Springer, 1970, 673.
[22]	Kousis P. Introduction to theory of spaces Hp. Mir, Moscow, 1984, 364.