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Functional models and asymptotically orthonormal sequences

Isabelle Chalendar, Emmanuel Fricain, Dan Timotin (2003)

Annales de l’institut Fourier

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.

Functional-analytic properties of Corson-compact spaces

S. Argyros, S. Mercourakis, S. Negrepontis (1988)

Studia Mathematica

Functionals Close to Each Other.

Béla Bollobás (1972)

Elemente der Mathematik

Functionals on function and sequence spaces connected with the exponential stability of evolutionary processes

Petre Preda, Alin Pogan, Ciprian Preda (2006)

Czechoslovak Mathematical Journal

The exponential stability property of an evolutionary process is characterized in terms of the existence of some functionals on certain function spaces. Thus are generalized some well-known results obtained by Datko, Rolewicz, Littman and Van Neerven.

Functions locally dependent on finitely many coordinates.

Petr Hájek, Václav Zizler (2006)

RACSAM

The notion of functions dependent locally on finitely many coordinates plays an important role in the theory of smoothness and renormings on Banach spaces, especially when higher smoothness (C∞) is involved. In this note we survey most of the main results in this area, and indicate many old as well as new open problems.

Further properties of Azimi-Hagler Banach spaces

Parviz Azimi, H. Khodabakhshian (2009)

Czechoslovak Mathematical Journal

Gabor meets Littlewood-Paley: Gabor expansions in $L^{p} (ℝ^{d})$

Karlheinz Gröchenig, Christopher Heil (2001)

Studia Mathematica

It is known that Gabor expansions do not converge unconditionally in $L^{p}$ and that $L^{p}$ cannot be characterized in terms of the magnitudes of Gabor coefficients. By using a combination of Littlewood-Paley and Gabor theory, we show that $L^{p}$ can nevertheless be characterized in terms of Gabor expansions, and that the partial sums of Gabor expansions converge in $L^{p}$ -norm.