Titlebook: Microlocal Analysis, Sharp Spectral Asymptotics and Applications V; Applications to Quan Victor Ivrii Book 2019 Springer Nature Switzerland

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Spectral Asymptotics for the Semiclassical Dirichlet to Neumann Operatort-to-Neumann operator. is defined to be .. Weobtain a leading asymptotic for the spectral counting function for. in an interval . as ., under the assumption that the measure of periodic billiardson . is zero. The asymptotic takes the form.where . is given explicitly by

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Asymptotics of the Ground State Energy in the Relativistic Settingsd, in particular, to derive relativistic Scott correction term and also Dirac, Schwinger and relativistic correction terms. Also we will prove that Thomas-Fermi density approximates the actual density of the ground state, which opens the way to estimate the excessive negative and positive charges an

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Complete Semiclassical Spectral Asymptotics for Periodic and Almost Periodic Perturbations of Constaator and .(.,?.) is a periodic or almost periodic perturbation.. In particular, a complete semiclassical asymptotics of the integrated density of states also holds. Further, we consider generalizations.

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100 years of Weyl’s Law the sharp asymptotics. We consider Weyl asymptotics, asymptotics with Weyl principal parts and correction terms and asymptotics with non-Weyl principal parts. Semiclassical microlocal analysis, propagation of singularities and related dynamics play crucial role..We start from the general theory, th

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of technique, developed by the author during more than 40 y.The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular,