Kyoto Journal of Mathematics

Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces

Pavel Dimovski, Stevan Pilipović, Bojan Prangoski, and Jasson Vindas

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Abstract

We introduce and study a number of new spaces of ultradifferentiable functions and ultradistributions and we apply our results to the study of the convolution of ultradistributions. The spaces of convolutors O'C*(Rd) for tempered ultradistributions are analyzed via the duality with respect to the test function spaces OC*(Rd) introduced in this article. We also study ultradistribution spaces associated to translation-invariant Banach spaces of tempered ultradistributions and use their properties to provide a full characterization of the general convolution of Roumieu ultradistributions via the space of integrable ultradistributions. We show that the convolution of two Roumieu ultradistributions T,SD'{Mp}(Rd) exists if and only if (φSˇ)TD'L1{Mp}(Rd) for every φD{Mp}(Rd).

Article information

Source
Kyoto J. Math. Volume 56, Number 2 (2016), 401-440.

Dates
Received: 3 September 2014
Revised: 17 February 2015
Accepted: 8 April 2015
First available in Project Euclid: 10 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1462901083

Digital Object Identifier
doi:10.1215/21562261-3478916

Mathematical Reviews number (MathSciNet)
MR3500846

Zentralblatt MATH identifier
1352.46039

Subjects
Primary: 46F05: Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35]
Secondary: 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) 46F10: Operations with distributions 46E10: Topological linear spaces of continuous, differentiable or analytic functions

Keywords
convolution of ultradistributions translation-invariant Banach space of tempered ultradistributions ultratempered convolutors Beurling algebra parametrix method

Citation

Dimovski, Pavel; Pilipović, Stevan; Prangoski, Bojan; Vindas, Jasson. Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces. Kyoto J. Math. 56 (2016), no. 2, 401--440. doi:10.1215/21562261-3478916. https://projecteuclid.org/euclid.kjm/1462901083


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