Domains of analytic existence in real Frechet spaces

• Autorzy: Mauer M.
• Języki publikacji: EN

Abstrakty

EN

If E is a real separable Frechet space, we prove that every non void domain Omega of E is open for a continuous semi-norm is a domain of analytic existence. In particular, every non void, open and convex subset Omega of E is a domain of analytic existence. Moreover, this result cannot be improved in the case of an arbitrary real separable Frechet space. In fact, in the space omega of real sequences, a non void domain Omega is a domain of analytic existence if and only if Omega is open for a continuous semi-norm.

Słowa kluczowe

EN

analytic function; domain of analytic existence; Frechet space

PL

funkcja analityczna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 1
• Strony: 7--19
• Opis fizyczny: Bibliogr. 5 poz.,

Twórcy

autor

Mauer M.

• Institute of Mathematics, University of Liege, Grande Traverse, 12 Sari-Tilman, Iicatiment B37, B-4000 Liege 1, Belgium

Bibliografia

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• [2] J. Bochnak, J. Siciak, Analytic functions in topological vector spaces, Studia Math., 39 (1971) 77--112.
• [3] M. Hervé, Analyticity in infinite dimensional spaces, de Gruyter Studies in Mathematics, 10 (1989).
• [4] M. Mauer, Domains of analytic existence in inductive limits of real separable normed spaces, Bull. Belg. Math. Soc., Simon Stevie, 5 (1998) 93-100.
• [5] J. Schmet s, M. VaIdivia, Domains of existence of R-analytic functions in real normed spaces, Bull. Pol. Acad.: Math., 41 (1993) 131-137.