Complex boundary value problems

Complex Symplectic Spaces and Boundary Value Problems

This paper presents a review and summary of recent research on the boundary value problems for linear ordinary and partial differential equations, with special attention to the investigations of the current authors emphasizing the applications of complex symplectic spaces. In the first part of the previous century, Stone and von Neumann formulated the theory of self-adjoint extensions of symmet...

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Nonlocal Boundary Value Problems

The theory of the nonlocal linear boundary value problems is still on the level of examples. Any attempt to encompass them by a unified scheme sticks upon the lack of general methods. Here we are to outline an algebraic approach to linear nonlocal boundary value problems. It is based on the notion of convolution of linear operator and on operational calculus on it. Our operators are right inver...

Discrete Boundary-value Problems

We consider multivariate sequences, deened by a partial linear recurrence equation together with appropriate boundary conditions. The domain of deenition of these sequences is the rst orthant of the integer lattice, restricted in some dimensions to an initial segment of the nonnegative integers. By means of the kernel method we obtain an explicit expression for the generating function of the so...