20525 Functional Analysis 1

Credits: 6 advanced credits in Mathematics

Prerequisites: Students must fulfill all English requirements and take bibliographic instruction in the Library.

Required: Infinitesimal Calculus I, Infinitesimal Calculus II, Linear Algebra I, Linear Algebra II, Ordinary Differential Equations I, as well as having accumulated about 50 credits in Mathematics

Recommended: Infinitesimal Calculus III, Measure Theory

Authors: Eli Levin, Vadim Grinstein

The course is structured along the lines of Basic Operator Theory, by I. Gohberg and S. Goldberg (Birkhäuser, 1981). Due to its level of sophistication, the course is recommended primarily to veteran Mathematics students. It may also be of interest to Physics students with suitable mathematical background.

Topics: Hilbert spaces, orthonormal systems, linear operators, linear functionals, the spectral theorem for compact self adjoint operators and applications, operator functions; Banach spaces, linear functionals, the Hahn-Banach theorem and applications, linear operators, the closed graph theorem and the uniform boundedness principle, applications, Fredholm’s alternative; The fixed point theorem, applications.

1A short non-credit seminar may be added to this course. See note under Mathematics seminars.