Schulze, Bert-Wolfgang Pseudo-differential boundary value problems, conical singularities and asymptotics. (English) Zbl 0810.35175 Mathematical Topics. 4. Berlin: Akademie Verlag. 580 p. (1994). This book contains the exposition of part of B.-W. Schulze’s work on the calculus of pseudo-differential operators on manifolds with singularities. More precisely, the book is devoted to the case of conical singularities and the study of boundary value problems. Related ideas are developed in [B.-W. Schulze, Pseudo-differential operators on manifolds with singularities (1991; Zbl 0747.58003)] by the same author, and the reader is sometimes referred to this book for proofs.The first part of the book is entitled “Mellin pseudo-differential operators”. There the author introduces and studies Sobolev-type spaces and pseudo-differential operators defined by means of the classical Mellin transform. Manifolds with conical singularities are introduced; ellipticity and parametrices of the pseudo-differential operators are discussed.In the second part of the book, entitled “Pseudo-differential boundary value problems”, the author first shows how to express usual pseudo- differential operators on a half axis in terms of his Mellin-type pseudo- differential operators. Then a boundary symbolic calculus (using Melling transform) is constructed. Attention is paid to the transmission property which was introduced in the study of pseudo-differential boundary value problems in the sixties. Reviewer: P.Godin (Bruxelles) Cited in 9 ReviewsCited in 39 Documents MSC: 35S15 Boundary value problems for PDEs with pseudodifferential operators 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations Keywords:Mellin pseudo-differential operators; Mellin transform; conical singularities; ellipticity; parametrices; pseudo-differential operators on a half axis; boundary symbolic calculus; transmission property Citations:Zbl 0747.58003 PDFBibTeX XMLCite \textit{B.-W. Schulze}, Pseudo-differential boundary value problems, conical singularities and asymptotics. Berlin: Akademie Verlag (1994; Zbl 0810.35175)