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This work explores various advanced topics in mathematical physics and operator theory, including the heat equation asymptotics of a generalized Ahlfors Laplacian on manifolds with boundaries and the contrasting behaviors of recurrent versus diffusive quantum systems under time-dependent Hamiltonians. It delves into spectral measures for Feller operators and provides a global perspective on locating quantum resonances. The text presents estimates for eigenvalues in elliptic problems and discusses quantum scattering in the presence of long-range magnetic fields. It addresses spectral invariance and submultiplicativity in Fréchet algebras, with applications to pseudo-differential operators and *-quantization. Key results include exponential decay of eigenfunctions for Kac's operator in higher dimensions and second-order perturbations of divergence-type operators exhibiting a spectral gap. The analysis extends to Weyl quantized relativistic Hamiltonians and spectral asymptotics for commuting operator families. Additionally, it examines pseudo-differential operators with negative definite symbols, one-dimensional Schrödinger operators with high barriers, and boundary value problems in angular domains. Insights into non-linear equations in cylindrical domains, stable asymptotics for Dirichlet problems, and Maslov operator calculus are also presented, alongside discussions on trace formulas and functional calculus for boundary value
Achat du livre
Operator Calculus and Spectral Theory, Michael Demuth
- Langue
- Année de publication
- 2012
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