Riesz bases of reproducing kernels in Fock-type spaces

DOI10.1017/S147474800900019XzbMath1198.30054arXiv0906.4815OpenAlexW2963139907MaRDI QIDQ3569365

Alexander Borichev, Yurij I. Lyubarskij

Publication date: 18 June 2010

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.4815

zbMATH Keywords

reproducing kernelsRiesz basesFock spaces

Mathematics Subject Classification ID

Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Bergman spaces and Fock spaces (30H20)

Related Items (30)

Unconditional bases of reproducing kernels for Fock spaces with nonradial weights ⋮ Spectral synthesis in Hilbert spaces of entire functions ⋮ On unconditional exponential bases in weighted spaces on interval of real axis ⋮ Unconditional bases in radial Hilbert spaces ⋮ Geometry of reproducing kernels in model spaces near the boundary ⋮ Sampling and interpolation in de Branges spaces with doubling phase ⋮ Complete interpolating sequences for the Gaussian shift-invariant space ⋮ Equivalent conditions for the existence of unconditional bases of reproducing kernels in spaces of entire functions ⋮ On unconditional bases of exponentials in weighted spaces on an interval of the real axis ⋮ Entire functions of sine type for convex apeirogons ⋮ On a sufficient condition for the existence of unconditional bases of reproducing kernels in Fock type spaces with nonradial weights ⋮ Fock type spaces with Riesz bases of reproducing kernels and de Branges spaces ⋮ Equivalent norms in Hilbert spaces with unconditional bases of reproducing kernels ⋮ On unconditional bases of reproducing kernels in Fock-type spaces ⋮ Bergman interpolation on finite Riemann surfaces. I: Asymptotically flat case ⋮ On unconditional exponential bases in weak weighted spaces on segment ⋮ Compact Carleson measures from sparse sequences ⋮ Necessary condition for the existence of unconditional bases of reproducing kernels for Hilbert spaces of entire functions ⋮ Volterra type integral operators and composition operators on model spaces ⋮ On Hilbert spaces of entire functions with unconditional bases of reproducing kernels ⋮ On a sufficient condition for the existence of unconditional bases of reproducing kernels in Hilbert spaces of entire functions ⋮ Riesz bases of reproducing kernels in small Fock spaces ⋮ Riesz bases of normalized reproducing kernels in Fock type spaces ⋮ Complete interpolating sequences for small Fock spaces ⋮ Geometry of radial Hilbert spaces with unconditional bases of reproducing kernels ⋮ Generating functions for bases in Hilbert spaces of entire functions ⋮ Unconditional bases in weakly weighted spaces of entire functions ⋮ On a criterion for the existence of unconditional bases of reproducing kernels in Fock spaces with radial regular weight ⋮ Sampling, interpolation and Riesz bases in small Fock spaces ⋮ Spectral synthesis in de Branges spaces

Cites Work

• Unnamed Item
• Sampling and interpolation in large Bergman and Fock spaces
• Sampling and interpolation of entire functions and exponential systems in convex domains
• Multipliers and weighted \(\bar\partial\)-estimates.
• The absence of unconditional bases of exponentials in Bergman spaces on non-polygonal domains
• Approximation of subharmonic functions
• On approximation of subharmonic functions
• Bergman kernel asymptotics for generalized Fock spaces

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