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.
| ISBN: | 9780821884874 |
| Publication date: | 30th March 2013 |
| Author: | A V Sobolev |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 104 pages |
| Series: | Memoirs of the American Mathematical Society |
| Genres: |
Differential calculus and equations |