A Riesz basis for Bargmann-Fock space related to sampling and interpolation
Copyright policy )A Riesz basis for Bargmann-Fock space related to sampling and interpolation
Let \(A^ p(C)\), \(1\leq p<\infty\) be the Bargmann-Fock space of entire functions as follows: \[ A^ p(C)=\left\{f\text{ entire: } \iint | f(z)|^ p e^{-\pi p| z|^ 2/2} dx dz<\infty\right\}. \] In this paper, the authors provide a surprisingly simple and explicit unconditional basis for \(A^ p(C)\) which is closely connected to the reproducing kernel and has the same structure as the Wilson type bases [\textit{I. Daubechies}, \textit{S. Jaffard} and \textit{J.-L. Journe}, SIAM J. Math. Anal. 22, No. 2, 554-572 (1991; Zbl 0754.46016)]. From this a new sampling and interpolation result for these spaces is derived.
- University of Connecticut United States
- George Mason University United States
unconditional basis, Banach algebras of differentiable or analytic functions, \(H^p\)-spaces, Bargmann-Fock space of entire functions, reproducing kernel, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Spaces of bounded analytic functions of one complex variable, Wilson type bases, Interpolation in approximation theory
unconditional basis, Banach algebras of differentiable or analytic functions, \(H^p\)-spaces, Bargmann-Fock space of entire functions, reproducing kernel, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Spaces of bounded analytic functions of one complex variable, Wilson type bases, Interpolation in approximation theory
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