Result: Representation theorems for tempered ultradistributions
Title:
Representation theorems for tempered ultradistributions
Source:
Publications de l'Institut Mathematique, Beograd. 65(79):142-160
Publisher Information:
Serbian Academy of Sciences and Arts (Srpska Akademija Nauka i Umetnosti - SANU), Mathematical Institute (Matematički Institut), Belgrade, 1999.
Publication Year:
1999
Subject Terms:
representation theorems, heat equation, Topological linear spaces of test functions, distributions and ultradistributions, boundary value problem, Beurling and Roumieu type tempered ultradistributions, Integral transforms in distribution spaces, Hyperfunctions, analytic functionals, tempered ultradistributions, heat kernel technique, Operations with distributions and generalized functions
Document Type:
Academic journal
Article
File Description:
application/xml
ISSN:
0350-1302
Access URL:
Accession Number:
edsair.dedup.wf.002..05c4c26e88b0c4c2039abc3e3b56a632
Database:
OpenAIRE
Further Information
In a series of papers, \textit{T. Matsuzawa} introduced the heat kernel technique [see e.g., Nagoya Math. J. 108, 53-66 (1987; Zbl 0636.46047)]. The authors of the paper under review use Matsuzawa's technique to obtain two characterizations of classes of both Beurling and Roumieu type tempered ultradistributions. Moreover, they prove that every solution of the heat equation with appropriate exponential growth defines an element of the corresponding class of spaces, and, conversely, that every element of these classes can be obtained as a boundary value of a solution of the heat equation with appropriate growth.