Premium
Quaternion fourier integral operators for spaces of generalized quaternions
Author(s) -
AlOmari Shrideh K. Q.,
Baleanu D.
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.5304
Subject(s) - quaternion , mathematics , fourier integral operator , convolution (computer science) , fourier transform , operator (biology) , operator theory , pure mathematics , fourier inversion theorem , mathematical analysis , generalized function , algebra over a field , fourier analysis , fractional fourier transform , geometry , biochemistry , chemistry , repressor , machine learning , artificial neural network , computer science , transcription factor , gene
This article aims to discuss a class of quaternion Fourier integral operators on certain set of generalized functions, leading to a method of discussing various integral operators on various spaces of generalized functions. By employing a quaternion Fourier integral operator on points closed to the origin, we introduce convolutions and approximating identities associated with the Fourier convolution product and derive classical and generalized convolution theorems. Working on such identities, we establish quaternion and ultraquaternion spaces of generalized functions, known as Boehmians, which are more general than those existed on literature. Further, we obtain some characteristics of the quaternion Fourier integral in a quaternion sense. Moreover, we derive continuous embeddings between the classical and generalized quaternion spaces and discuss some inversion formula as well.