ANALYTIC AND PROBABILISTIC METHODS IN MATHEMATICAL PHYSICS II
basics of differential and integral calculus and of the theory of partial differential equations
Oral test which consists in verifying the ability to express oneself in correct mathematical language and to demonstrate some of the theorems encountered during the course.
The aim of the course is to provide students with the basic theoretical tools of the theory of unbounded linear operators in Hilbert spaces; in particular of the Schroedinger operators.
The result to be achieved at the end of the course is that the student knows how to use the basic techniques of the theory of unbounded linear operators, having also developed a good intuition on the meaning of the concepts learned.
Unbounded, closed and closable linear operators in Banach spaces. Symmetric, self-adjoint, essentially self-adjoint operators in Hilbert spaces. The spectral theorem for self-adjoint operators, the Stone theorem. Perturbations of self-adjoint operators, the Rellich-Kato theorem. Quadratic forms and Friedrichs’ theorem. Some spectral theory for Schroedinger operators. Compact operators and the invariance of the essential spectrum. The relationship between spectrum and dynamics: the RAGE theorem.
Frontal lessons: 64 hours. In the lectures the theoretical notions are developed and the techniques necessary for the application of the theory to the solution of problems in Mathematical Physics are described.
to make an appointment write to posilicano@uninsubria.it
Professors
Borrowers
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Degree course in: MATHEMATICS
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Degree course in: PHYSICS
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Degree course in: PHYSICS