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.
