Weakly Singular Integral Inequalities and Composition Formulas in Weyl Calculus

Abstract

We show the solutions of certain integral equations, by means of operators of arbitrary order, and fractional differintegral equations. Complete analysis of bounded variation penalty methods is shown for ill-posed problems with more considerations to the autoconvolution equations, total variation constraints and exact determination of the density function by its autoconvolution coefficients. The free multiplicities in branching problems are obtained with unitary highest modules. Existence of compact quotients of homogenous spaces, measurably proper actions, and decay of matrix coefficients with tempered actions are established. In addition, conformal geometry and branching laws for representations concerned with minimal nilpotent orbits are investigated. We give explicit solutions of fractional integral, fractional differential equations and differential equations involving Erdelyi-Kober operators, with high applications on the generalized Gronwall inequality. We also find explicit bounds for weakly singular integral inequalities with applications to fractional differential and integral equations. We study the integro-differential equations of first order with autoconvolution integral structure and show the theory and present the general class of autoconvoluation equations of the third kind. We construct the composition formulas in the Weyl calculus.