An elementary integral solution operator for the Cauchy-Riemann equations on pseudoconvex domains in ${\bf C}\sp{n}$

An effective method for approximating the solution of singular integral equations with Cauchy kernel type

In present paper, a numerical approach for solving Cauchy type singular integral equations is discussed. Lagrange interpolation with Gauss Legendre quadrature nodes and Taylor series expansion are utilized to reduce the computation of integral equations into some algebraic equations. Finally, five examples with exact solution are given to show efficiency and applicability of the method. Also, w...

On the Solution of a Class of Cauchy Integral Equations

The ǫ in (2) (missing in Ref. [3]) is needed to guarantee the continuity of ã(λ) (Carlsonian interpolation of the an’s) at λ = −1/2 + iν, ν ∈ R (see next formula (15)). Let us remind the reader that these results in the case p = 0 (i.e. fn = an) are due to Stein and Wainger [9]; however, these authors do not formulate the requirements on the Taylor coefficients an by the use of the Hausdorff co...

An Integral Operator Solution to the Matrix Toda Equations

In previous work the author found solutions to the Toda equations that were expressed in terms of determinants of integral operators. Here it is observed that a simple variant yields solutions to the matrix Toda equations. As an application another derivation is given of a differential equation of Sato, Miwa and Jimbo for a particular Fredholm determinant. During the last twenty years, beginnin...

The Cauchy-riemann Equations and Differential Geometry

The Cauchy-Riemann Operator in Infinite Dimensional Spaces

In this survey article we present a sketch of the tecliniques which allowed to advance into the problem of solving the a-problem in infinite dimensional spaces. As an example we show how tite O-problem for a holomorphic (O,2)-form on a D.F.N. space can be solved by using the solution of the a-problem for a holomorphic (O,2)-form on a separable Hilbert space. For further detajís we refer to SORA...