Functional Analysis and Applications Seminar 

07/11/2003, 15:00 — 16:00 — Room P3.10, Mathematics Building
Frank-Olme Speck, Instituto Superior Técnico, U.T. Lisboa

Diffraction by Rectangular Wedges with Different Face Impedances

Some basic hitherto open boundary value problems are treated by a new potential approach, using so-called reproducing half-line potentials. It involves symmetry properties, operator relations, factorization methods and normalization techniques for convolution type operators with symmetry that were recently developed by various members of the CEMAT operator theory group. Interior wedge problems of normal type for the Helmholtz equation could be completely analyzed and explictly solved by analytical formulas which also allow fine results about the solutions' regularity properties. It turns out that these results are also good for reducing exterior wedge problems in a most efficient way to scalar boundary pseudodifferential equations. However, their nature is much more complicated and cumbersome compared with the class of interior wedge diffration problems. Only very particular boundary conditions allow a detailed comparable analysis. The lecture is based upon common work with L. P. Castro and F. S. Teixeira.