Lebedev–Skalskaya transforms on certain function spaces and associated pseudo-differential operators
U. K. Mandal, Akhilesh Prasad
Abstract
In this paper, some basic results and notations related to Lebedev–Skalskaya transforms (LS-transforms) are introduced and then estimates of translation and convolution operators associated to LS-transform are obtained. Continuity of LS-transforms on Lebesgue space as well as on function spaces Sβ,k and Gα,k are discussed. Pseudo-differential operators in terms of LS-transforms are defined and their integral representations have been studied in various ways. Moreover, their estimates in Lebesgue space are obtained. At the end, some applications have been discussed.
Topics & Concepts
MathematicsConvolution (computer science)Lebesgue integrationLp spaceIntegral transformStandard probability spaceFunction spaceDifferential operatorConvolution theoremDifferential (mechanical device)Pure mathematicsSpace (punctuation)Function (biology)Translation (biology)Fourier integral operatorMathematical analysisReal-valued functionAlgebra over a fieldFourier transformOperator theoryFractional Fourier transformFourier analysisBanach spaceBiologyChemistryMachine learningLinguisticsArtificial neural networkAerospace engineeringGenePhilosophyEngineeringBiochemistryMessenger RNAEvolutionary biologyComputer scienceMathematical Analysis and Transform MethodsMathematical functions and polynomialsDigital Filter Design and Implementation