Pseudo-Differential Operators With Discontinuous Symbols: Widom's Conjecture

(Memoirs of the American Mathematical Society)

514KlQM04FL._SX356_BO1,204,203,200_ Author A. V. Sobolev
Isbn 9780821884874
File size 883.23KB
Year 2013
Pages 104
Language English
File format PDF
Category Mathematics

Book Description:

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.

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