it is well known that the parabolic partial differential equationsin two or more space dimensions with overspecified boundary data,feature in the mathematical modeling of many phenomena. in thisarticle, an inverse problem of determining an unknowntime-dependent source term of a parabolic equation in generaldimensions is considered. employing some transformations, wechange the inverse problem to...

We study certain generalized Cauchy integral formulas for gradients of solutions to second order divergence form elliptic systems, which appeared in recent work by P. Auscher and A. Rosén. These are constructed through functional calculus and are in general beyond the scope of singular integrals. More precisely, we establish such Cauchy formulas for solutions u with gradient in weighted L2(R 1+...

We characterize boundedness and compactness of weighted composition operators from the space of Cauchy integral transforms to logarithmic weighted-type spaces. We also manage to compute norm of weighted composition operators acting between these spaces.

A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential for...