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The Kontorovich‐Lebedev transform and its associated pseudodifferential operator
Author(s) -
Prasad Akhilesh,
Mandal Upain Kumar
Publication year - 2017
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.4593
Subject(s) - mathematics , convolution (computer science) , integral transform , hartley transform , standard probability space , fractional fourier transform , operator (biology) , lp space , space (punctuation) , convolution theorem , mathematical analysis , mellin transform , riesz transform , lebesgue integration , representation (politics) , fourier transform , pure mathematics , banach space , fourier analysis , computer science , biochemistry , chemistry , repressor , machine learning , politics , artificial neural network , transcription factor , law , political science , gene , operating system
In this paper, we obtained some useful estimates for convolution corresponding to Kontorovich‐Lebedev transform (KL‐transform) in Lebesgue space. Some continuity theorems for translation, convolution, and KL‐transform in test function space H ( R + ) are discussed. Then an integral representation of pseudodifferential operator involving KL‐transform is found out, and its estimates in Lebesgue space is obtained. At the end, some applications of KL‐transform and its convolution are discussed.