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A quadratic‐phase integral operator for sets of generalized integrable functions
Author(s) -
AlOmari Shrideh K. Q.,
Baleanu Dumitru
Publication year - 2020
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.6181
Subject(s) - mathematics , integrable system , quadratic equation , operator (biology) , convolution (computer science) , fourier integral operator , pure mathematics , exponential function , mathematical analysis , algebra over a field , operator theory , repressor , biochemistry , chemistry , geometry , machine learning , artificial neural network , transcription factor , computer science , gene
In this paper, we aim to discuss the classical theory of the quadratic‐phase integral operator on sets of integrable Boehmians. We provide delta sequences and derive convolution theorems by using certain convolution products of weight functions of exponential type. Meanwhile, we make a free use of the delta sequences and the convolution theorem to derive the prerequisite axioms, which essentially establish the Boehmian spaces of the generalized quadratic‐phase integral operator. Further, we nominate two continuous embeddings between the integrable set of functions and the integrable set of Boehmians. Furthermore, we introduce the definition and the properties of the generalized quadratic‐phase integral operator and obtain an inversion formula in the class of Boehmians.