Canonical potential and L<sup>p</sup>-Sobolev space involving linear canonical Fourier transform
Akhilesh Prasad, Amit Kumar
Abstract
The main objective of this paper is to enrich the theoretical system of the linear canonical Fourier transform (LCFT) by introducing the canonical potential Jm,A and corresponding Lp-Sobolev space. Moreover, the Schwartz-type space SA is introduced. Further, pseudo-differential operator (PDO) is defined and obtained its another integral representation. The Lp-boundedness result for the pseudo-differential operator associated with the LCFT is discussed. Some applications of Sobolev-type spaces HAm,p and HAm,p are given.
Topics & Concepts
MathematicsSobolev spaceFourier transformOperator (biology)Mathematical analysisPure mathematicsType (biology)Space (punctuation)Differential operatorPseudo-differential operatorCanonical formSemi-elliptic operatorBiologyTranscription factorRepressorChemistryBiochemistryPhilosophyLinguisticsGeneEcologyHypoelliptic operatorMathematical Analysis and Transform MethodsImage and Signal Denoising MethodsAdvanced Numerical Analysis Techniques