Titlebook: Microlocal Analysis and Precise Spectral Asymptotics; Victor Ivrii Book 1998 Springer-Verlag Berlin Heidelberg 1998 Dirac.Microlocal analy

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Victor IvriiThe pathbreaking work of Victor Ivrii in the last ten years represents very difficult mathematics..Because of its technical difficulty and its size, it cannot be expected to sell to a large audience..

樸素

Propagation of Singularities near the Boundaryormulated in terms of auxiliary functions as was theorem 2.1.2. In section 3.2 we prove some statements similar to those of the second part of section 2.1 and section 2.2. Section 3.3 is similar to section 2.3 and section 2.4. Finally, in Appendix A we prove some auxiliary assertions.

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978-3-642-08307-5Springer-Verlag Berlin Heidelberg 1998

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Microlocal Analysis and Precise Spectral Asymptotics978-3-662-12496-3Series ISSN 1439-7382 Series E-ISSN 2196-9922

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恭維

Introduction to Semiclassical Microlocal Analysisnotion of oscillation front sets and related topics (in section 1.3) and a functional calculus for .-pseudo-differential operators (in section 1.4). Proofs are mostly absent since all the results of this chapter are either trivial consequences of the results proven in [H?rmander 1] or can be proven

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Meander

Standard Local Semiclassical Spectral Asymptotics in the Interior of a Domain . → +0 only; more precisely, in this chapter we are interested in asymptotics of the spectral . (restriction to the diagonal of the Schwartz kernel of the spectral projector) and its spatial means in the ball .(0, 1/2) under the assumption that the ball .(0, 1) is contained in the domain. Moreover,

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Standard Local Semiclassical Spectral Asymptotics near the Boundaryersects the boundary of the domain in a part of the boundary which is smooth. This chapter consists of four sections corresponding to first four sections of Chapter 4. Namely, section 5.1 is devoted to the preliminary analysis; here we obtain rough estimates of the spectral function. More precisely,