Lp-integr ability, supports of Fourier transforms and uniqueness for convolution equations

M. L. Agranovsky; E. K. Narayanan

doi:10.1007/s00041-004-0986-4

L^p-integr ability, supports of Fourier transforms and uniqueness for convolution equations

M. L. Agranovsky, E. K. Narayanan

Department of Mathematics

Harish Chandra Research Institute

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

17 Scopus citations

Abstract

It is proved that a nonzero function is not in L^p(Rⁿ) with p ≤ 2n/d if its Fourier transform is supported by a d - dimensional submanifold. It is shown that the assertion fails for p > 2n/d and d ≥ n/2. The result is applied for obtaining uniqueness theorems for convolution equations in L^p-spaces.

Original language	English
Pages (from-to)	315-324
Number of pages	10
Journal	Journal of Fourier Analysis and Applications
Volume	10
Issue number	3
DOIs	https://doi.org/10.1007/s00041-004-0986-4
State	Published - 2004

Keywords

Convolution equations
Distributions
Evolution equations
Injectivity
Supports of fourier transforms

Access to Document

10.1007/s00041-004-0986-4

Cite this

@article{f2230ae5fdf34b40822dd2a5a459c8bc,

title = "Lp-integr ability, supports of Fourier transforms and uniqueness for convolution equations",

abstract = "It is proved that a nonzero function is not in Lp(Rn) with p ≤ 2n/d if its Fourier transform is supported by a d - dimensional submanifold. It is shown that the assertion fails for p > 2n/d and d ≥ n/2. The result is applied for obtaining uniqueness theorems for convolution equations in Lp-spaces.",

keywords = "Convolution equations, Distributions, Evolution equations, Injectivity, Supports of fourier transforms",

author = "Agranovsky, {M. L.} and Narayanan, {E. K.}",

year = "2004",

doi = "10.1007/s00041-004-0986-4",

language = "אנגלית",

volume = "10",

pages = "315--324",

journal = "Journal of Fourier Analysis and Applications",

issn = "1069-5869",

publisher = "Birkhauser Boston",

number = "3",

}

TY - JOUR

T1 - Lp-integr ability, supports of Fourier transforms and uniqueness for convolution equations

AU - Agranovsky, M. L.

AU - Narayanan, E. K.

PY - 2004

Y1 - 2004

N2 - It is proved that a nonzero function is not in Lp(Rn) with p ≤ 2n/d if its Fourier transform is supported by a d - dimensional submanifold. It is shown that the assertion fails for p > 2n/d and d ≥ n/2. The result is applied for obtaining uniqueness theorems for convolution equations in Lp-spaces.

AB - It is proved that a nonzero function is not in Lp(Rn) with p ≤ 2n/d if its Fourier transform is supported by a d - dimensional submanifold. It is shown that the assertion fails for p > 2n/d and d ≥ n/2. The result is applied for obtaining uniqueness theorems for convolution equations in Lp-spaces.

KW - Convolution equations

KW - Distributions

KW - Evolution equations

KW - Injectivity

KW - Supports of fourier transforms

UR - http://www.scopus.com/inward/record.url?scp=3543032806&partnerID=8YFLogxK

U2 - 10.1007/s00041-004-0986-4

DO - 10.1007/s00041-004-0986-4

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:3543032806

SN - 1069-5869

VL - 10

SP - 315

EP - 324

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 3

ER -

L^p-integr ability, supports of Fourier transforms and uniqueness for convolution equations

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this