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A certain integral-recurrence equation with discrete-continuous auto-convolution

Mircea I. Cîrnu (2011)

Archivum Mathematicum

Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations.

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.

A spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on n

E. K. Narayanan, S. Thangavelu (2006)

Annales de l’institut Fourier

We prove a spectral Paley-Wiener theorem for the Heisenberg group by means of a support theorem for the twisted spherical means on n . If f ( z ) e 1 4 | z | 2 is a Schwartz class function we show that f is supported in a ball of radius B in n if and only if f × μ r ( z ) = 0 for r > B + | z | for all z n . This is an analogue of Helgason’s support theorem on Euclidean and hyperbolic spaces. When n = 1 we show that the two conditions f × μ r ( z ) = μ r × f ( z ) = 0 for r > B + | z | imply a support theorem for a large class of functions with exponential growth. Surprisingly enough,this latter...

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