University of Connecticut

Course Info

MATH 5131: Functional Analysis II

Description: Spectral theory of unbounded self-adjoint and normal operators on Hilbert spaces. Quadratic forms. Examples and counterexamples of self-adjoint operators. Spectral theory of differential operators with constant coefficients. Unitary and positivity preserving operator semigroups, resolvents, Trotter product formula, Hille-Yosida theorem. Other topics in functional analysis at the choice of the instructor (e.g. applications to probability and quantum mechanics, introduction to von Neumann algebras and non-commutative integration).

Prerequisites: MATH 5111.

Credits: 3

MATH 5131 - Section 1: Functional Analysis II

Description: In the first part of the class, we will cover the spectral theorem for bounded and unbounded self-adjoint operators. In the second half of the class, we will study the geometry of Banach spaces with the goal of proving the Johnson-Lindenstrauss Lemma and Dvoretzky’s theorem. In order to do so we will develop tools from isoperimetry, concentration of measure and Haar measure. Instructor: Sean Li

Credits: 3

Sections: Spring 2018 on Storrs Campus

PSCourseID Course Sec Comp Time Room Instructor
15144 5131 001 Lecture TuTh 12:30:00 PM-01:45:00 PM HALL104 Sean Li