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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Unconditional bases in $ L\sp 2(0,a)$


Author: Sergeĭ V. Hruščëv
Journal: Proc. Amer. Math. Soc. 99 (1987), 651-656
MSC: Primary 46J15; Secondary 46E30, 47B35
MathSciNet review: 877034
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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)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0877034-X
PII: S 0002-9939(1987)0877034-X
Keywords: Toeplitz operator, Muckenhoupt condition, unconditional bases
Article copyright: © Copyright 1987 American Mathematical Society