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Some remarks on short‐time Fourier integral operators and classes of rapidly decaying functions
Author(s) -
AlOmari Shrideh K. Q.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5379
Subject(s) - mathematics , convolution (computer science) , fourier transform , fourier integral operator , operator (biology) , convolution theorem , fourier inversion theorem , mathematical analysis , inversion (geology) , fourier analysis , convolution power , space (punctuation) , discrete time fourier transform , operator theory , fractional fourier transform , computer science , biochemistry , chemistry , paleontology , repressor , structural basin , machine learning , biology , artificial neural network , transcription factor , gene , operating system
In this article, we extend the space of rapidly decaying functions to a space of rapidly decaying Boehmians. We provide convolution products, convolution theorems and generate their associated spaces of Boehmian. Then, we define the short‐time Fourier integral operator on the Boehmian spaces. Moreover, we show that the short‐time Fourier integral operator of the Boehmian is a sequentially continuous mapping that preserves certain desired properties. An inversion formula and some injections have also been obtained.