Methods of Spectral Analysis in Mathematical Physics (eBook)

Spectral Asymptotics of Percolation Hamiltonians on Amenable Cayley Graphs.- On Inverse Problems for Finite Trees.- Wave Operators for Nonlocal Sturm-Liouville Operators with Trivial Potential.- Semiclassical Results for Ideal Fermion Systems. A Review.- Quadratic Hamiltonians and Their Renormalization.- Jacobi Matrices: Eigenvalues and Spectral Gaps.- Eigenvalue Estimates for the Aharonov-Bohm Operator in a Domain.- The Ablowitz-Ladik Hierarchy Revisited.- On Dirichlet-to-Neumann Maps and Some Applications to Modified Fredholm Determinants.- Higher Derivatives of Spectral Functions Associated with One-Dimensional Schrödinger Operators.- On the Boundary Value Problem for p-parabolic Equations.- On the Rank One Dissipative Operator and the Parseval Formula.- On the Schrödinger Operator with Limit-periodic Potential in Dimension Two.- Similarity Problem for Non-self-adjoint Extensions of Symmetric Operators.- Inverse Scattering Problem for a Special Class of Canonical Systems and Non-linear Fourier Integral. Part I: Asymptotics of Eigenfunctions.- Remark on the Compensation of Singularities in Krein’s Formula.- On Some Properties of Infinite-dimensional Elliptic Coordinates.- Finite Difference Operators with a Finite-Band Spectrum.- Connections Between Dynamical Systems and Crossed Products of Banach Algebras by ?.- Born-Oppenheimer-type Approximations for Degenerate Potentials: Recent Results and a Survey on the Area.- The Ornstein-Uhlenbeck Semigroup in Bounded and Exterior Lipschitz Domains.