Stability of the bases and frames reproducing kernels in model spaces

Anton Baranov

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Displaying similar documents to “Stability of the bases and frames reproducing kernels in model spaces”

Functional models and asymptotically orthonormal sequences

Isabelle Chalendar, Emmanuel Fricain, Dan Timotin (2003)

Annales de l’institut Fourier

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Suppose $H^{2}$ is the Hardy space of the unit disc in the complex plane, while $Θ$ is an inner function. We give conditions for a sequence of normalized reproducing kernels in the model space $K_{Θ} = H^{2} ⊖ Θ H^{2}$ to be asymptotically close to an orthonormal sequence. The completeness problem is also investigated.

Bases in the spaces $C$ and $L^{1}$

S. J. Szarek (1979-1980)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

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Subsequences of frames

R. Vershynin (2001)

Studia Mathematica

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Every frame in Hilbert space contains a subsequence equivalent to an orthogonal basis. If a frame is n-dimensional then this subsequence has length (1 - ε)n. On the other hand, there is a frame which does not contain bases with brackets.