Codomains for the Cauchy-Riemann and Laplace operators inℝ2

The Cauchy-riemann Equations and Differential Geometry

On symmetric Cauchy-Riemann manifolds

The Riemannian symmetric spaces play an important role in different branches of mathematics. By definition, a (connected) Riemannian manifold M is called symmetric if, to every a ∈ M , there exists an involutory isometric diffeomorphism sa:M → M having a as isolated fixed point in M (or equivalently, if the differential dasa is the negative identity on the the tangent space Ta = TaM of M at a)....

Vector-valued Laplace Transforms and Cauchy Problems

This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are stu...

Nvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition

Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...

Cauchy-stieltjes and Riemann-stielt Jes Integrals