Reed and Simon,
Functional Analysis I.
Academic Press, 1980.
Related Literature
Stein,
Singular Integrals and Differentiability
Properties of Functions.
Princeton University Press, 1970.
de la Harpe et Valette,
La Propriété (T) de Kazhdan pour les
Groupes Localement Compacts.
Astérisque 175, 1989;
distributed by the American Mathematical Society.
Prerequisites.
Intended for advanced graduate students.
Topics.
This course will present several topics,
from elliptic partial differential equations
to ergodic theory,
with spectral theory and unitary representations as
an underlying theme. Possible topics include:
Distributions and Fourier Analysis
Test functions, convolutions
Distributions and duality
Fourier transform and Sobolev spaces
Singular integral operators
Elliptic equations
Prime number theorem
Operator algebras
Banach algebras and C* algebras
The Gelfand representation
Functional calculus
Positive operators
Self-adjoint operators
Unitary operators and representations
Ergodic Theory
The Birkhoff ergodic theorem
Geodesic flow on hyperbolic surfaces
Hopf's proof of ergodicity and mixing
Kazhdan's property T for SL_3(R)
Expanding graphs
Grades.
Graduate students who have passed their
quals are excused from a grade for this course.
Grades for other students will be based on homework and a final paper.
Calendar.
4 Feb (Th)
First class.
30 Mar, 1 Apr (Tu,Th)
No class - spring break.
6 May (Th)
Last class. Final papers due.
Course home page: http://math.harvard.edu/~ctm/math212b