Boundary Value Problems and Singular Pseudo-Differential OperatorsThis 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. |
Common terms and phrases
analogous manner arbitrary As(X assertion assume asymptotic sum asymptotic types Banach spaces c₁ compact operator complete symbol cone constant continuous embeddings corresponding cut-off function w(t define Definition denote diffeomorphism discrete asymptotics elements elliptic excision function finite finite-dimensional fixed follows formal adjoint Fréchet space Fréchet topology Fredholm operator G₁ Green operators H₁ H₂ H³(R H³(X Hilbert spaces implies induces continuous operators isomorphism kernel L²(R L²(R+ Lemma Let us set manifold Mellin Moreover neighbourhood notation obtain Op(a Op(b open set operator family operator-valued symbols order µ parameter-dependent parametrix Proof properly supported Proposition pseudo-differential operators push-forward R¹+9 Remark respect S(R+ satisfying semi-norm Sobolev spaces subspace suffices symbol of order Theorem transmission property w₁ weakly discrete