A method of constructing conditional bases of power functions in certain banach spaces of analytic functions

被引：0
作者：
Petrov A.N. [1 ]
机构：
来源：
Journal of Mathematical Sciences | 2000年 / 101卷 / 3期
关键词：
Banach Space; Toeplitz Operator; Unconditional Basis; Basic Family; Space Mult;
D O I：
10.1007/BF02673740
中图分类号：
学科分类号：
摘要：
In this note, a method of constructing conditional exponential bases in some. Banach spaces of analytic functions is presented. The method of constructing basic families due to Figà-Talamanca is generalized. Concrete applications and examples of conditional basic families in the space of multipliers of power series with the sequence of Taylor coefficients from lp, in the space of multipliers of Cauchy-type integrals, and in other spaces are given. ©2000 Kluwer Academic/Plenum Publishers.
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页码：3149 / 3165
页数：16
相关论文
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  • [1] Figà-Talamanca, A., An example in the theory of lacunary Fourier series (1970) Boll. Della Unione Mat. Ital., 3, pp. 375-378
  • [2] Suslikov, O.G., On trigonometric Fourier series with gaps (1973) Vestn. MGU, pp. 46-55
  • [3] Gaposhkin, V.F., On unconditional bases in the spaces Lp(p ≥ 1) (1958) Usp. Mat. Nauk, pp. 179-184
  • [4] Gurarii, V.I., Matsaev, V.I., Lacunary sequences of powers in the spaces C and Lp (1966) Izv. Akad. Nauk SSSR, Ser. Mat., 30, pp. 3-14
  • [5] Vinogradov, S.A., Bases of exponentials and free interpolation in Banach spaces with L p-norm (1976) Zap. Nauchn. Semin. LOMI, 65, pp. 17-68
  • [6] Vinogradov, S.A., Properties of multipliers of Cauchy-Stieltjes integrals and some factorization problems for analytic functions (1980) Am. Math. Soc. (Transl. (2)), 115, pp. 1-32
  • [7] Aleksandrov, A.B., Essays on non locally convex Hardy classes (1981) Led. Notes Math., 864, pp. 1-89
  • [8] Zygmund, A., (1959) Trigonometric Series, 1. , Cambridge Univ. Press
  • [9] Kahane, J.-P., (1968) Some Random Series of Functions, , D. C. Heath & Co., Lexington, Mass
  • [10] Nikolskii, N.K., On spaces and algebras of Toeplitz matrices acting in lp (1966) Sib. Mat. Zh., 7, pp. 146-158
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