Advanced Real Analysis
Math 212b / Tu Th 10-11:30 / 216 SC
Harvard University - Spring 2006
Curtis T McMullen
Functional Analysis, 2nd ed.
Lectures on Functional Analysis.
Springer-Verlag, 1974 (unfortunately, out of print)
Dover reprint, 1990.
- Reed and Simon,
Functional Analysis I.
Academic Press, 1980.
Directed to graduate students.
Lebesgue measure and integral, general topology,
and theory of linear operators between Banach spaces
will be assumed.
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.
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:
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 exams.
Collaboration is encouraged on homework.
Exam work should be based only on course materials and done
without the help of others.
- Distributions and Fourier Analysis
Test functions, convolutions
Distributions and duality
Fourier transform and Sobolev spaces
Singular integral operators
Fluid flow in the plane
Prime number theorem
- Operator algebras
Banach algebras and C* algebras
The Gelfand representation
Unitary operators and representations
Ergodic theory, Property T, expanding graphs,
and further topics
| 2 Feb (Th)
|| First class.
| 28, 30 Mar (Tu,Th)
|| No class - spring break.
| 4 May (Th)
|| Last class.
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