Kyoto Journal of Mathematics

Multiplication of periodic hyperfunctions via harmonic regularization and applications

V. Valmorin

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Abstract

We build a locally convex algebra of real analytic functions defined in a strip of the Poincaré half-plane in which a class of periodic hyperfunctions on the real line is topologically embedded. This is accomplished via a harmonic regularization method. In this algebra, we can give a sense to differential problems involving products of hyperfunctions which are a priori not defined in the classical setting. Some examples and an application are given.

Article information

Source
Kyoto J. Math., Volume 59, Number 2 (2019), 267-292.

Dates
Received: 11 May 2015
Revised: 9 January 2017
Accepted: 13 February 2017
First available in Project Euclid: 8 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1546916421

Digital Object Identifier
doi:10.1215/21562261-2018-0011

Mathematical Reviews number (MathSciNet)
MR3960294

Zentralblatt MATH identifier
07080105

Subjects
Primary: 32A45: Hyperfunctions [See also 46F15]
Secondary: 35L05: Wave equation 42A16: Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30} 46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)

Keywords
Fourier series product of periodic hyperfunctions locally convex algebras wave equation

Citation

Valmorin, V. Multiplication of periodic hyperfunctions via harmonic regularization and applications. Kyoto J. Math. 59 (2019), no. 2, 267--292. doi:10.1215/21562261-2018-0011. https://projecteuclid.org/euclid.kjm/1546916421


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