Research ArticleOpen AccessGoogle Scholar indexed
On Basis Properties of Degenerate Exponential System
Non-Harmonic Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan
- 1 Non-Harmonic Analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan
Applied Mathematics·Volume 03 (2012)·Pages 1963–1966·Published 12 December 2012·DOI10.4236/am.2012.312269
Copy link · social · email
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.
KeywordsSystem of ExponentsDegenerationBasicityCompletenessMinimality
- A. Zigmund, “Trigonometric Series,” Vol. 1, Mir, Moscow, 1965.
- A. Zigmund, “Trigonometric Series,” Vol. 2, Mir, Moscow, 1965.
- R. Edwards, “Fourier Series in a Modern Exposition,” Vol. 1, Mir, Moscow, 1985.
- R. Edwards, “Fourier Series in a Modern Exposition,” Vol. 2, Mir, Moscow, 1985.
- N. K. Bari, “Biorthogonal Systems and Bases in Hilbert Space,” Mathematics, Vol. 148, No. 4, 1951, pp. 69-107.
- K. I. Babenko, “On Conjugated Functions,” DAN SSSR, Vol. 62, No. 2, 1948, pp. 157-160.
- V. F. Gaposhkin, “One Generalization of M. Riesz Theorem on Conjugated Functions,” Matematicheskii Sbornik, Vol. 46, No. 3, 1958, pp. 111-115.
- 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.
- E. I. Moiseev, “On Basicity of Systems of Cosines and Sines in Weight Space,” Differential Equations, Vol. 34, No. 1, 1998, pp. 40-44.
- 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.
- 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.
- 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.
- 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.
- J. Garnett, “Bounded Analytic Functions,” Mir, Moscow, 1984.
- E. S. Golubeva, “The System of Weighted Exponentials with Power Weights,” Natural Sciences, Vol. 83, No. 2, 2011, pp. 15-25.
- M. G. Krein, “Functional Analysis,” Nauka, Moscow, 1972