Landau's necessary density conditions for the Hankel transform

Luís Daniel Abreu; Afonso S. Bandeira

doi:10.1016/j.jfa.2011.11.024

Landau's necessary density conditions for the Hankel transform

Luís Daniel Abreu, Afonso S. Bandeira

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We will prove an analogue of Landau's 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.

Original language	English (US)
Pages (from-to)	1845-1866
Number of pages	22
Journal	Journal of Functional Analysis
Volume	262
Issue number	4
DOIs	https://doi.org/10.1016/j.jfa.2011.11.024
State	Published - Feb 15 2012

Keywords

Bessel functions
Beurling-Landau density
Fourier-Bessel frames
Hankel transform
Sampling and interpolation

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2011.11.024

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title = "Landau's necessary density conditions for the Hankel transform",

abstract = "We will prove an analogue of Landau's 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.",

keywords = "Bessel functions, Beurling-Landau density, Fourier-Bessel frames, Hankel transform, Sampling and interpolation",

author = "Abreu, {Lu{\'i}s Daniel} and Bandeira, {Afonso S.}",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (L.D. Abreu), [email protected] (A.S. Bandeira). 1 Currently at NuHAG, University of Vienna, in (FWF) project “Frames and Harmonic Analysis”. This research was partially supported by CMUC/FCT and FCT project “Frame Design” PTDC/MAT/114394/2009, POCI 2010 and FSE. 2 Part of this work was done while the second author was at Department of Mathematics of University of Coimbra supported by the research grant BII/FCTUC/C2008/CMUC. Partially supported by CMUC/FCT and FCT project “Frame Design” PTDC/MAT/114394/2009, POCI 2010 and FSE.",

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doi = "10.1016/j.jfa.2011.11.024",

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T1 - Landau's necessary density conditions for the Hankel transform

AU - Abreu, Luís Daniel

AU - Bandeira, Afonso S.

N1 - Funding Information: * Corresponding author. E-mail addresses: [email protected] (L.D. Abreu), [email protected] (A.S. Bandeira). 1 Currently at NuHAG, University of Vienna, in (FWF) project “Frames and Harmonic Analysis”. This research was partially supported by CMUC/FCT and FCT project “Frame Design” PTDC/MAT/114394/2009, POCI 2010 and FSE. 2 Part of this work was done while the second author was at Department of Mathematics of University of Coimbra supported by the research grant BII/FCTUC/C2008/CMUC. Partially supported by CMUC/FCT and FCT project “Frame Design” PTDC/MAT/114394/2009, POCI 2010 and FSE.

PY - 2012/2/15

Y1 - 2012/2/15

N2 - We will prove an analogue of Landau's 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.

AB - We will prove an analogue of Landau's 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.

KW - Bessel functions

KW - Beurling-Landau density

KW - Fourier-Bessel frames

KW - Hankel transform

KW - Sampling and interpolation

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SP - 1845

EP - 1866

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 4

ER -

Landau's necessary density conditions for the Hankel transform

Abstract

Keywords

ASJC Scopus subject areas

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