A constructive approach to the solution of a class of boundary value problems of mixed type

In this article we discuss the solution of boundary value problems which are described by the linear integrodifferential equation $\text{?xu}\text{?t}\text{(t, x) + u(t, x) ?}\text{1}\text{π}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∝}{}_{\mathrm{?\infty }}{}^{\mathrm{\infty }}\text{exp}\text{(?y}{}^2\text{) u(t, y) dy = 0}$, where t∈J?$\text{R}$, x∈$\text{R}$. We interpret the equation in functional form as an ordinary differential equation for the mapping u:J→L₂(R,μ), where L₂(R,μ) is a weighted L₂-space. Emphasis is on the constructive aspects of the solution and on finding representations of the relevant isomorphisms.