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This book covers the analysis of pseudo-differential operators on manifolds with conical points and edges. The standard singular integral operators on the half-axis as well as boundary value problems on smooth manifolds are treated as particular cone and wedge theories. It features a self-contained presentation of the cone pseudo-differential calculus; a general method for pseudo-differential analysis on manifolds with edges for arbitrary model cones in spaces with discrete and continuous asymptotics; the presentation of the algebra of boundary value problems with the transmission property, obtained as a modification of the general wedge theory; and a new exposition of the pseudo-differential calculus with operator-valued symbols, based on twisted homogeneity as well as on parameter-dependent theories and reductions of orders.
Pseudo-Differential Operators.
Mellin Pseudo-Differential Operators on Manifolds with Conical Singularities.
Pseudo-Differential Calculus on Manifolds with Edges.
Boundary Value Problems.
Bibliography.
Index.
Presented in this book is the study of pseudo-differential operators on singular spaces and developments of the concept of ellipticity in operator algebra, and in particular studies of these on manifolds with boundary, conical or edge singularities, or with non-compact "exits to infinity".
This book covers the analysis of pseudo-differential operators on manifolds with conical points and edges. The standard singular integral operators on the half-axis as well as boundary value problems on smooth manifolds are treated as particular cone and wedge theories. It features a self-contained presentation of the cone pseudo-differential calculus; a general method for pseudo-differential analysis on manifolds with edges for arbitrary model cones in spaces with discrete and continuous asymptotics; the presentation of the algebra of boundary value problems with the transmission property, obtained as a modification of the general wedge theory; and a new exposition of the pseudo-differential calculus with operator-valued symbols, based on twisted homogeneity as well as on parameter-dependent theories and reductions of orders.
Pseudo-Differential Operators. Mellin Pseudo-Differential Operators on Manifolds with Conical Singularities. Pseudo-Differential Calculus on Manifolds with Edges. Boundary Value Problems. Bibliography. Index.
