Displaying similar documents to “Functional models and asymptotically orthonormal sequences”

Stability of the bases and frames reproducing kernels in model spaces

Anton Baranov (2005)

Annales de l'institut Fourier

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We study the bases and frames of reproducing kernels in the model subspaces K Θ 2 = H 2 ⊖ Θ H 2 of the Hardy class H 2 in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels k λ n ( z ) = ( 1 - Θ ( λ n ) ¯ Θ ( z ) ) / ( z - λ ¯ n ) under “small” perturbations of the points λ n . We propose an approach to this problem based on the recently obtained estimates of derivatives in the spaces K Θ 2 and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.

On summability of measures with thin spectra

Maria Roginskaya, Michaël Wojciechowski (2004)

Annales de l’institut Fourier

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We study different conditions on the set of roots of the Fourier transform of a measure on the Euclidean space, which yield that the measure is absolutely continuous with respect to the Lebesgue measure. We construct a monotone sequence in the real line with this property. We construct a closed subset of ℝ d which contains a lot of lines of some fixed direction, with the property that every measure with spectrum contained in this set is absolutely continuous. We also give examples of sets...

Bounds of Riesz Transforms on L p Spaces for Second Order Elliptic Operators

Zhongwei Shen (2005)

Annales de l’institut Fourier

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Let ℒ = -div ( A ( x ) ∇ ) be a second order elliptic operator with real, symmetric, bounded measurable coefficients on ℝ n or on a bounded Lipschitz domain subject to Dirichlet boundary condition. For any fixed p > 2 , a necessary and sufficient condition is obtained for the boundedness of the Riesz transform ∇ ( ℒ ) - 1 / 2 on the L p space. As an application, for 1 < p < 3 + ϵ , we establish the L p boundedness of Riesz transforms on Lipschitz domains for operators with V M O coefficients. The range of p is sharp. The closely related boundedness...

Riesz means of Fourier transforms and Fourier series on Hardy spaces

Ferenc Weisz (1998)

Studia Mathematica

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Elementary estimates for the Riesz kernel and for its derivative are given. Using these we show that the maximal operator of the Riesz means of a tempered distribution is bounded from H p ( ℝ ) to L p ( ℝ ) (1/(α+1) < p < ∞) and is of weak type (1,1), where H p ( ℝ ) is the classical Hardy space. As a consequence we deduce that the Riesz means of a function ⨍ ∈ L 1 ( ℝ ) converge a.e. to ⨍. Moreover, we prove that the Riesz means are uniformly bounded on H p ( ℝ ) whenever 1/(α+1) < p < ∞. Thus, in case ⨍ ∈ H p ( ℝ ) , the Riesz...

Traces and the F. and M. Riesz theorem for vector fields

Shiferaw Berhanu, Jorge Hounie (2003)

Annales de l’institut Fourier

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This work studies conditions that insure the existence of weak boundary values for solutions of a complex, planar, smooth vector field L . Applications to the F. and M. Riesz property for vector fields are discussed.