符号不连续的伪微分算子的拟经典渐近性：Widom猜想
Quasi-classical asymptotics for pseudo-differential operators with discontinuous symbols: Widom's Conjecture
摘要：
1982年H. Widom证明了该公式的多维推广，用于伪微分算子$A$，符号$a(\bx, \bxi)$在两个变量中都具有跳跃间断。在1990年，他证明了猜想的特殊情况下，跳跃的任何两个变量发生在一个超平面。本文给出了Widom猜想在任意光滑有界曲面上的一个证明，该证明是在两个变量都有符号跳跃的假设下给出的。
英文摘要：
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 generalization of that formula for a pseudo-differential operator $A$ with a symbol $a(\bx, \bxi)$ 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 gives 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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