We will prove an analogue of Landau's necessary conditions [Necessary density
conditions for sampling and interpolation of certain entire functions, Acta
Math. 117 (1967).] for spaces of functions whose Hankel transform is supported
in a measurable subset S of the positive semi-axis. As a special case,
necessary density conditions for the existence of Fourier-Bessel frames are
obtained.Comment: To appear on J. Funct. Analysi

Afonso S. Bandeira

Bergman

Boas

Ciaurri

Daubechies

Gröchenig

Guadalupe

Higgins

Landau

Luís Daniel Abreu

Marzo

Ortega-Cerdá

Ramanathan

Rauhut

Rawn

Seip

Tracy

Watson

Young

English

arXiv

AbstractWe will prove an analogue of Landauʼs necessary conditions [H.J. Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math. 117 (1967) 37–52] for spaces of functions whose Hankel transform is supported in a measurable subset S of the positive semi-axis. As a special case, necessary density conditions for the existence of Fourier–Bessel frames are obtained

Abreu, Luís Daniel

Bandeira, Afonso S.

Elsevier - Publisher Connector 

Landauʼs necessary density conditions for the Hankel transform 

We will prove an analogue of Landau’s necessary conditions [Necessary
density conditions for sampling and interpolation of certain entire functions, Acta
Math. 117 (1967).] for spaces of functions whose Hankel transform is supported in
a measurable subset S of the positive semi-axis. As a special case, necessary density
conditions for the existence of Fourier-Bessel frames are obtained. In the course of
our proof we obtain estimates for some eigenvalues which arise in Tracy and Widom
work [Level spacing distributions and the Bessel kernel. Comm. Math. Phys. 161
(1994), no. 2, 289–309.

Bandeira, Afonso

Estudo Geral