Schwartz kernel theorem in algebras of generalized functions

• Autorzy: Vincent Valmorin
• Języki publikacji: EN

Abstrakty

EN

A new approach to the generalization of Schwartz's kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of $G^{∞}$-generalized functions class are given. A straightforward relationship between the classical and the generalized versions of Schwartz's kernel theorem is established.

Kategorie tematyczne

• 46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
• 47G10: Integral operators
• 46F10: Operations with distributions
• 47B34: Kernel operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 88
• Numer: 1
• Strony: 285-296

Daty

wydano

2010

Twórcy

autor

Vincent Valmorin

• Département de Mathématiques et Informatique, Université des Antilles et de la Guyane, Campus de Fouillole, 97159 Pointe à Pitre Cedex, France

Identyfikatory

DOI

10.4064/bc88-0-23