Sampling and interpolation for a lacunary spectrum

Yu Lyubarskii; I. Spitkovsky

doi:10.1017/S0308210500030602

Sampling and interpolation for a lacunary spectrum

Yu Lyubarskii, I. Spitkovsky

Mathematics

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

Abstract

We reduce the problem of constructing a sampling and interpolating set for the space of functions with limited multi-band spectra to a problem of invertibility of certain convolution operators on a system of intervals, and obtain an example of such a set located in a horizontal strip along the real axis. We also study the question of sampling of a signal with two-banded spectra via its values at the union of two arithmetic progressions.

Original language	English (US)
Pages (from-to)	77-87
Number of pages	11
Journal	Royal Society of Edinburgh - Proceedings A
Volume	126
Issue number	1
DOIs	https://doi.org/10.1017/S0308210500030602
State	Published - 1996

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1017/S0308210500030602

Cite this

@article{a2b0e6bc124c4d128a2b5fbd38f3b599,

title = "Sampling and interpolation for a lacunary spectrum",

abstract = "We reduce the problem of constructing a sampling and interpolating set for the space of functions with limited multi-band spectra to a problem of invertibility of certain convolution operators on a system of intervals, and obtain an example of such a set located in a horizontal strip along the real axis. We also study the question of sampling of a signal with two-banded spectra via its values at the union of two arithmetic progressions.",

author = "Yu Lyubarskii and I. Spitkovsky",

note = "Funding Information: * Partly supported by a grant from the Air Force Office of Scientific t Partly supported by an NFS grant DMS-9401848.",

year = "1996",

doi = "10.1017/S0308210500030602",

language = "English (US)",

volume = "126",

pages = "77--87",

journal = "Royal Society of Edinburgh - Proceedings A",

issn = "0308-2105",

publisher = "Cambridge University Press",

number = "1",

}

TY - JOUR

T1 - Sampling and interpolation for a lacunary spectrum

AU - Lyubarskii, Yu

AU - Spitkovsky, I.

N1 - Funding Information: * Partly supported by a grant from the Air Force Office of Scientific t Partly supported by an NFS grant DMS-9401848.

PY - 1996

Y1 - 1996

N2 - We reduce the problem of constructing a sampling and interpolating set for the space of functions with limited multi-band spectra to a problem of invertibility of certain convolution operators on a system of intervals, and obtain an example of such a set located in a horizontal strip along the real axis. We also study the question of sampling of a signal with two-banded spectra via its values at the union of two arithmetic progressions.

AB - We reduce the problem of constructing a sampling and interpolating set for the space of functions with limited multi-band spectra to a problem of invertibility of certain convolution operators on a system of intervals, and obtain an example of such a set located in a horizontal strip along the real axis. We also study the question of sampling of a signal with two-banded spectra via its values at the union of two arithmetic progressions.

UR - http://www.scopus.com/inward/record.url?scp=21344440796&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344440796&partnerID=8YFLogxK

U2 - 10.1017/S0308210500030602

DO - 10.1017/S0308210500030602

M3 - Article

AN - SCOPUS:21344440796

SN - 0308-2105

VL - 126

SP - 77

EP - 87

JO - Royal Society of Edinburgh - Proceedings A

JF - Royal Society of Edinburgh - Proceedings A

IS - 1

ER -

Sampling and interpolation for a lacunary spectrum

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this