Book

Spectral analysis, differential equations, and mathematical physics

Differential equationsMathematical physicsOrdinary differential equations -- Dynamic equations on time scales or measure chains -- Dynamic equations on time scales or measure chainsOrdinary differential equations -- Ordinary differential operators -- General spectral theoryPartial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theoryPartial differential equations -- Hyperbolic equations and systems -- Initial value problems for first-order hyperbolic systemsFunctional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theoremsOperator theory -- General theory of linear operators -- General (adjoints, conjugates, products, inverses, domains, ranges, etc.).Operator theory -- Special classes of linear operators -- Jacobi (tridiagonal) operators (matrices) and generalizationsQuantum theory -- Quantum field theory; related classical field theories -- Constructive quantum field theoryQuantum theory -- General mathematical topics and methods in quantum theory -- Selfadjoint operator theory in quantum theory, including spectral analysisSystems theory; control -- Stochastic systems and control -- Stochastic systems, general