On a space of smooth functions on a convex unbounded set in ℝn admitting holomorphic extension in ℂn

• Autorzy: Il’dar Musin , Polina Yakovleva
• Języki publikacji: EN

Abstrakty

EN

For some given logarithmically convex sequence M of positive numbers we construct a subspace of the space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in ℝn. Due to the conditions on M each function of this space admits a holomorphic extension in ℂn. In the current article, the space of holomorphic extensions is considered and Paley-Wiener type theorems are established. To prove these theorems, some auxiliary results on extensions of holomorphic functions satisfying some weighted L 2-bounds in a domain of holomorphy in ℂn are obtained with the aid of L. Hörmander’s method of L 2-bounds for the $$\bar \partial$$ operator. Also, some new facts on the Fourier-Laplace transform of tempered distributions complementing some well-known results of V.S. Vladimirov are employed.

Słowa kluczowe

EN

Ultradistributions; Tempered distributions; Fourier-Laplace transform; Holomorphic functions; Entire functions

Kategorie tematyczne

• 32A07: Special domains (Reinhardt, Hartogs, circular, tube)
• 32W05: ∂ ¯ and ∂ ¯ -Neumann operators
• 32A15: Entire functions
• 32A70: Functional analysis techniques \SeeMainly{}
• 32A10: Holomorphic functions
• 46E10: Topological linear spaces of continuous, differentiable or analytic functions
• 46F05: Topological linear spaces of test functions, distributions and ultradistributions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 2
• Strony: 665-692

Daty

wydano

2012-04-01

online

2012-01-18

Twórcy

autor

Il’dar Musin

• Russian Academy of Sciences

autor

Polina Yakovleva

• Russian Academy of Sciences

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0142-8