Biorthogonal multicomponent finite integral transformation and its application to boundary value problems of mechanics (Q1357959)

We construct and justify a new class of vector finite integral transformations based on multicomponent correlation of biorthogonality of eigenvector-functions of two homogeneous boundary value problems, related to each other by Lagrange equality. We formulate a structure algorithm on an example of a closed solution of axially symmetric dynamic problem for an inhomogeneous circular plate. An essential moment in the procedure of the structure algorithm is the selection of an adjoint operator without which it is impossible to solve non-selfadjoint linear problems of mathematical physics by decomposing in eigenvector-functions.