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

22 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

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10.1007/s00041-004-0986-4

Cite this

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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.",

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AU - Agranovsky, M. L.

AU - Narayanan, E. K.

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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

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JF - Journal of Fourier Analysis and Applications

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ER -

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

Abstract

Keywords

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