{"product_id":"pseudo-differential-operators-with-discontinuous-symbols-widom-s-conjecture","title":"Pseudo-Differential Operators with Discontinuous Symbols: Widom's Conjecture","description":"\u003cp\u003eRelying 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 $a(\\mathbf{x}, \\boldsymbol{\\xi})$ 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.\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003eAuthor:\u003c\/b\u003e Aleksandr Vladimirovich Sobolev\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePublisher:\u003c\/b\u003e American Mathematical Soc.\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePublished:\u003c\/b\u003e 2013-02-26\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePages:\u003c\/b\u003e 116\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Soc.","offers":[{"title":"Default Title","offer_id":62808709595507,"sku":"9780821884874","price":200.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0987\/0812\/8115\/files\/content_50e47ebd-3830-4925-96b4-d476218f4530.jpg?v=1777969188","url":"https:\/\/readaura.store\/products\/pseudo-differential-operators-with-discontinuous-symbols-widom-s-conjecture","provider":"Read Aura","version":"1.0","type":"link"}