# A microlocal F. and M. Riesz theorem with applications.

Revista Matemática Iberoamericana (1989)

- Volume: 5, Issue: 1-2, page 21-36
- ISSN: 0213-2230

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topBrummelhuis, Raymondus G. M.. "A microlocal F. and M. Riesz theorem with applications.." Revista Matemática Iberoamericana 5.1-2 (1989): 21-36. <http://eudml.org/doc/39382>.

@article{Brummelhuis1989,

abstract = {Consider, by way of example, the following F. and M. Riesz theorem for Rn: Let μ be a finite measure on Rn whose Fourier transform μ* is supported in a closed convex cone which is proper, that is, which contains no entire line. Then μ is absolutely continuous (cf. Stein and Weiss [SW]). Here, as in the sequel, absolutely continuous means with respect to Lebesque measure. In this theorem one can replace the condition on the support of μ* by a similar condition on the wave front set WF(μ) of μ, while keeping the same conclusion. The resulting microlocal F. and M. Riesz theorem can be applied with great flexibility to derive F. and M. Riesz theorems for measures on Lie groups, measures satisfying partial differential equations, etc. This is, essentially, the program of this paper.},

author = {Brummelhuis, Raymondus G. M.},

journal = {Revista Matemática Iberoamericana},

keywords = {Análisis funcional; Teoría de la medida; microlocal F. and M. Riesz theorem; finite measure; wave front set; absolutely continuous; local space},

language = {eng},

number = {1-2},

pages = {21-36},

title = {A microlocal F. and M. Riesz theorem with applications.},

url = {http://eudml.org/doc/39382},

volume = {5},

year = {1989},

}

TY - JOUR

AU - Brummelhuis, Raymondus G. M.

TI - A microlocal F. and M. Riesz theorem with applications.

JO - Revista Matemática Iberoamericana

PY - 1989

VL - 5

IS - 1-2

SP - 21

EP - 36

AB - Consider, by way of example, the following F. and M. Riesz theorem for Rn: Let μ be a finite measure on Rn whose Fourier transform μ* is supported in a closed convex cone which is proper, that is, which contains no entire line. Then μ is absolutely continuous (cf. Stein and Weiss [SW]). Here, as in the sequel, absolutely continuous means with respect to Lebesque measure. In this theorem one can replace the condition on the support of μ* by a similar condition on the wave front set WF(μ) of μ, while keeping the same conclusion. The resulting microlocal F. and M. Riesz theorem can be applied with great flexibility to derive F. and M. Riesz theorems for measures on Lie groups, measures satisfying partial differential equations, etc. This is, essentially, the program of this paper.

LA - eng

KW - Análisis funcional; Teoría de la medida; microlocal F. and M. Riesz theorem; finite measure; wave front set; absolutely continuous; local space

UR - http://eudml.org/doc/39382

ER -

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