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On Basis Properties of Degenerate Exponential System

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DOI: 10.4236/am.2012.312269    2,640 Downloads   3,970 Views   Citations
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ABSTRACT

Exponential systems of the form are considered, where is a degenerate coefficient, is a set of all integers and . The basis properties of these systems in , when, generally speaking, doesn’t satisfy the Muckenhoupt condition are investigated.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Zahira, "On Basis Properties of Degenerate Exponential System," Applied Mathematics, Vol. 3 No. 12, 2012, pp. 1963-1966. doi: 10.4236/am.2012.312269.

References

[1] A. Zigmund, “Trigonometric Series,” Vol. 1, Mir, Moscow, 1965.
[2] A. Zigmund, “Trigonometric Series,” Vol. 2, Mir, Moscow, 1965.
[3] R. Edwards, “Fourier Series in a Modern Exposition,” Vol. 1, Mir, Moscow, 1985.
[4] R. Edwards, “Fourier Series in a Modern Exposition,” Vol. 2, Mir, Moscow, 1985.
[5] N. K. Bari, “Biorthogonal Systems and Bases in Hilbert Space,” Mathematics, Vol. 148, No. 4, 1951, pp. 69-107.
[6] K. I. Babenko, “On Conjugated Functions,” DAN SSSR, Vol. 62, No. 2, 1948, pp. 157-160.
[7] V. F. Gaposhkin, “One Generalization of M. Riesz Theorem on Conjugated Functions,” Matematicheskii Sbornik, Vol. 46, No. 3, 1958, pp. 111-115.
[8] K. S. Kazaryan and P. I. Lizorkin, “Multipliers, Bases and Unconditional Bases in the Weighted Spaces B and SB,” Proceedings of the Steklov Institute of Mathematics, Vol. 187, 1989, pp. 111-130.
[9] E. I. Moiseev, “On Basicity of Systems of Cosines and Sines in Weight Space,” Differential Equations, Vol. 34, No. 1, 1998, pp. 40-44.
[10] E. I. Moiseev, “The Basicity in the Weight Space of a System of Eigen Functions of a Differential Operator,” Differential Equations, Vol. 35, No. 2, 1999, pp. 200-205.
[11] B. T. Bilalov and S. G. Veliyev, “On Completeness of Exponent System with Complex Coefficients in Weight Spaces,” Transactions of the NAS of Azerbaijan, Vol. 25, No. 7, 2005, pp. 9-14.
[12] B. T. Bilalov and S. G. Veliyev, “Bases of Eigen Functions of Two Discontinuous Differential Operators,” Differential Equations, Vol. 42, No. 9, 2006, pp. 190-192.
[13] S. S. Pukhov and A. M. Sedletskii, “Bases of Exponents, Sines and Cosines in Weight Spaces on Finite Interval,” Doklady Akademii nauk. Rossijskaa akademia nauk, Vol. 425, No. 4, 2009, pp. 452-455.
[14] J. Garnett, “Bounded Analytic Functions,” Mir, Moscow, 1984.
[15] E. S. Golubeva, “The System of Weighted Exponentials with Power Weights,” Natural Sciences, Vol. 83, No. 2, 2011, pp. 15-25.
[16] M. G. Krein, “Functional Analysis,” Nauka, Moscow, 1972

  
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