Includes bibliographical references (pages 103-104) and index.
Introduction Main result Estimates for PDO's with smooth symbols Trace-class estimates for operators with non-smooth symbols} Further trace-class estimates for operators with non-smooth symbols A Hilbert-Schmidt class estimate Localisation Model problem in dimension one Partitions of unity, and a reduction to the flat boundary Asymptotics of the trace (9.1) Proof of Theorem 2.9 Closing the asymptotics: Proof of Theorems 2.3 and 2.4 Appendix 1: A lemma by H. Widom Appendix 2: Change of variables Appendix 3: A trace-class formula Appendix 4: Invariance with respect to the affine change of variables Bibliography.
(source: Nielsen Book Data)
Relying on the known two-term quasiclassical asymptotic formula for the trace of the function f(A) of a Wiener-Hopf type operator A in dimension one, in 1982 H. Widom conjectured a multi-dimensional generalisation of that formula for a pseudo-differential operator A with a symbol a(x, ?) having jump discontinuities in both variables. In 1990 he proved the conjecture for the special case when the jump in any of the two variables occurs on a hyperplane. The present paper provides a proof of Widom's Conjecture under the assumption that the symbol has jumps in both variables on arbitrary smooth bounded surfaces. (source: Nielsen Book Data)