Thema Deutsch. Zwischen Text und Interpretation. Textanalyse
Classical boundary integral equations arising from the potential
theory and acoustics (Laplace and Helmholtz equations) are derived.
Using the parametrization of the boundary these equations take a
form of periodic pseudodifferential equations. A general theory of
periodic pseudodifferential equations and methods of solving are
developed, including trigonometric Galerkin and collocation
methods, their fully discrete versions with fast solvers,
quadrature and spline based methods. The theory of periodic
pseudodifferential operators is presented in details, with
preliminaries (Fredholm operators, periodic distributions, periodic
Sobolev spaces) and full proofs. This self-contained monograph can
be used as a textbook by graduate/postgraduate students. It also
contains a lot of carefully chosen exercises.