Boundary Value Problems and Singular Pseudo-Differential Operators
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.
18 pages matching Riemannian metric in this book
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Mellin pseudodifferential operators on manifolds with
Pseudodifferential calculus on manifolds with edges
3 other sections not shown
A G R+ algebra analogous manner analogous result holds apply As(A As(X assertion assume asymptotic sum asymptotic types Banach spaces boundary value problems calculus carrier choose compact operator compact set complete symbol cone conormal symbols constant continuous embeddings converges define Definition denote diffeomorphism differential operators elements elliptic excision function finite finite-dimensional fixed follows formal adjoint Frechet space Frechet topology Fredholm operator Green operators Hilbert spaces homogeneous principal implies induces continuous operators isomorphism kernel Lemma Let us set Mellin transform modulo Moreover notation obtain Op(a op+(a open set operator family operator-valued symbols parameter-dependent parametrix particular partition of unity properly supported Proposition pseudo-differential operators Remark respect Riemannian metric Rn+1 S(R+ satisfying scalar product Schulze Section sequence smoothing Sobolev spaces subspace suffices symbol of order tends to zero transmission property weakly discrete asymptotics write yields