Unconditional bases in $L^ 2(0,a)$
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- by Sergeĭ V. Hruščëv PDF
- Proc. Amer. Math. Soc. 99 (1987), 651-656 Request permission
Abstract:
A method is given for producing unconditional bases in subspaces ${K_\theta } = {H^2} \ominus \theta {H^2}$ of the Hardy space ${H^2},\theta$ being an inner function in the upper half-plane. For $\theta = \exp {\text {(}}iaz)$ the space ${K_\theta }$ is the Fourier-Laplace transform of ${L^2}(0,a)$, which allows us to establish a necessary and sufficient condition for certain families of functions (including exponentials) to constitute unconditional bases in ${L^2}(0,a)$.References
-
B. S. Pavlov, Basicity of an exponential system and Muckenhoupt condition, Soviet Math. Dokl. 20 (1979), 655-659.
N. K. Nikol’skiĭ, Bases of exponential functions and values of reproducing kernels, Soviet Math. Dokl. 21 (1980), 937-941.
- S. V. Hruščëv, N. K. Nikol′skiĭ, and B. S. Pavlov, Unconditional bases of exponentials and of reproducing kernels, Complex analysis and spectral theory (Leningrad, 1979/1980) Lecture Notes in Math., vol. 864, Springer, Berlin-New York, 1981, pp. 214–335. MR 643384
- S. V. Hruščev, The Regge problem for strings, unconditionally convergent eigenfunction expansions, and unconditional bases of exponentials in $L^2(-T,T)$, J. Operator Theory 14 (1985), no. 1, 67–85. MR 789378 G. M. Gubreev, A basis property of families of the Mittag-Leffler functions, Dzhrbashyan’s transform, and the Muckenhoupt condition, Funktsional. Anal. i Prilozhen. 20:3 (1986). A. Erdélyi, Higher transcendental functions, vol. 3 (Bateman Manuscript Project), McGraw-Hill, New York.
- Harold Widom, Inversion of Toeplitz matrices. II, Illinois J. Math. 4 (1960), 88–99. MR 130572
- John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
- I. M. Gel’fand and G. E. Shilov, Generalized functions. Vol. I: Properties and operations, Academic Press, New York-London, 1964. Translated by Eugene Saletan. MR 0166596 N. K. Nikol’skiĭ and B. S. Pavlov, Eigenvector bases, characteristic functions and interpolation problems in Hardy’s ${H^2}$-space, Soviet Math. Dokl. 10 (1969), 138-141.
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 651-656
- MSC: Primary 46J15; Secondary 46E30, 47B35
- DOI: https://doi.org/10.1090/S0002-9939-1987-0877034-X
- MathSciNet review: 877034