On Basis Properties of Degenerate Exponential System

Affiliation(s)

Non-Harmonic Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.

Non-Harmonic Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.

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.

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.

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.

M. Zahira, "On Basis Properties of Degenerate Exponential System,"

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

[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