Generalized Fourier expansions for distributions and ultradistributions

Autores: S.N. Melikhov
Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 12, Nº 2, 1999, págs. 349-379
Idioma: inglés
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Resumen
- Let Dw(Pa)' be a space of distributions or ultradistributions of Beurling type on the p-dimensional parallelepiped Pa:=Ppj=1[-aj,aj]ÌRp. We investigate the following problems:
  
  1) When can any element of Dw(Pa)' be expanded in absolutely convergent series in a system of generalized exponentials (el(n))nÎNp with special exponents l(n), nÎNp.
  
  2) When can a sequence of the coefficients (cn)nÎNp in an expansionu=SnÎNp cnel(n) be chosen so that it depends in a continuous and linear way on uÎDw(Pa)', where 0