Open AccessApplication of the dual space of Gelfand-Shilov spaces of Beurling type
Author(s) -
Ala Qadomi,
Maysam Abu-Dalu,
Sa’ud Al-Sa’di,
Hamed M. Obiedat
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.50603
Subject(s) - mathematics , space (punctuation) , dual (grammatical number) , pure mathematics , semigroup , type (biology) , sigma , prime (order theory) , action (physics) , beta (programming language) , alpha (finance) , exponential type , mathematical analysis , physics , combinatorics , philosophy , computer science , ecology , linguistics , construct validity , statistics , quantum mechanics , biology , programming language , psychometrics
Using a previously obtained structure theorem of Gelfand-Shilov spaces $\Sigma _{\alpha }^{\beta }$ of Beurling type of ultradistributions, we prove that these ultradistributions can be represented as an initial values of solutions of the heat equation by describing the action of the Gauss-Weierstrass semigroup on the dual space $(\Sigma _{\alpha }^{\beta})^{\prime }.$