Mellin operators in a pseudodifferential calculus for boundary value problems on manifolds with edges
Elmar Schrohe, B.‐W. Schulze · Birkhäuser Basel eBooks · 1998
As an integral part of a pseudodifferential calculus for boundary value problems on manifolds with edges we introduce the algebra of Mellin operators. They represent the typical operators near the edge. In fact we show how to associate an operator-valued Mellin symbol to an arbitrary edge-degenerate pseudodifferential boundary value problem, the so-called ‘Mellin quantization’ procedure. Furthermore, we introduce a class of adequate Sobolev spaces based on the Mellin transform on which these operators act continuously. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.