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Schwartz kernel theorem in algebras of generalized functions

100%

Valmorin V.

Banach Center Publications

2010

tom 88

nr 1

285-296

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.

Sequence spaces with exponent weights. Realizations of Colombeau type algebras

55%

Delcroix A., Hasler M., Pilipović S., Valmorin V.

Instytut Matematyczny Polskiej Akademii Nauk

We give a description of various algebras of generalized functions based on the introduction of pseudo-ultranorms on spaces of sequences in given locally convex function algebras. We study sheaf properties of these algebras, needed for microlocal analysis, and also consider regularity theory, functoriality and different concepts of association and weak equality in a unified setting. Using this approach, we also give new results on embeddings of ultradistribution and hyperfunction spaces into corresponding algebras of generalized functions.

Ograniczanie wyników

1 Banach Center Publications

2 Valmorin V.

1 Delcroix A.

1 Hasler M.

1 Pilipović S.

1 2010

1 2007

Wyniki wyszukiwania

Schwartz kernel theorem in algebras of generalized functions

Sequence spaces with exponent weights. Realizations of Colombeau type algebras