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INICIO | 18 de abril de 2024
  

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

Título inglés A microlocal F. and M. Riesz theorem with applications.
Título español Un teorema de F. y M. Riesz microlocal con aplicaciones.
Autor/es Brummelhuis, Raymondus G. M.
Organización Dep. Math. Univ. Wisconsin, Madison (Wisconsin), Estados Unidos
Revista 0213-2230
Publicación 1989, 5 (1-2): 21-36, 11 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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.
Clasificación UNESCO 120220
Palabras clave español Análisis funcional ; Teoría de la medida
Código MathReviews MR1057336
Código Z-Math Zbl 0714.58055
Icono pdf Acceso al artículo completo
Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
rmm()icmat.es