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A Phragmén-Lindelöf type quasi-analyticity principle

Grzegorz Łysik (1997)

Studia Mathematica

Quasi-analyticity theorems of Phragmén-Lindelöf type for holomorphic functions of exponential type on a half plane are stated and proved. Spaces of Laplace distributions (ultradistributions) on ℝ are studied and their boundary value representation is given. A generalization of the Painlevé theorem is proved.

A q-analogue of complete monotonicity

Anna Kula (2008)

Colloquium Mathematicae

The aim of this paper is to give a q-analogue for complete monotonicity. We apply a classical characterization of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity, adapted to the q-situation. The method due to Maserick and Szafraniec that does not need moments turns out to be useful. A definition of a q-moment sequence appears as a by-product.

A remark on the asymmetry of convolution operators

Saverio Giulini (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A convolution operator, bounded on L q ( n ) , is bounded on L p ( n ) , with the same operator norm, if p and q are conjugate exponents. It is well known that this fact is false if we replace n with a general non-commutative locally compact group G . In this paper we give a simple construction of a convolution operator on a suitable compact group G , wich is bounded on L q ( G ) for every q [ 2 , ) and is unbounded on L p ( G ) if p [ 1 , 2 ) .

A sheaf of Boehmians

Jonathan Beardsley, Piotr Mikusiński (2013)

Annales Polonici Mathematici

We show that Boehmians defined over open sets of ℝⁿ constitute a sheaf. In particular, it is shown that such Boehmians satisfy the gluing property of sheaves over topological spaces.

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