Theory of Functions of a Real Variable II, Spring 2008
                                            Math 6321.

This course is a continuation of Math 6320 and the prerequisites for this course are a good knowledge
of Lebesgue measure and integration and of the topology of complete metric spaces.

This semester classes will be in AH 301  on  MW 5.30 - 7 pm. 

The syllabus includes the following topics.

  1.   Hilbert and Banach spaces,  properties and examples.
  2.   Orthonormal bases, Fourier series and the geometry of Hilbert spaces.
  3.   L^p spaces  and the fundamental inequalities of analysis.
  4.   Spaces of continuous functions, Arzela-Ascoli and Stone-Weierstrass theorems.
  5.   Dual spaces, the Hahn-Banach theorem, weak convergence and completeness.
  6.   Properties of continuous linear operators on Banach spaces.
  7.   Weak differentiation and Hilbert-Sobolev spaces.

The text-book is An Introduction to Hilbert Space by Nicholas Young, published by Cambridge
University Press. Despite the title it covers some   material on Banach spaces but we will not follow
this text very closely. Three more advanced texts that cover much of the material  are

Real Analysis, Modern Techniques and their Applications by Gerald B. Folland, published by
Wiley-Interscience,
Real Analysis III, Measure Theory, Integration and Hilbert Spaces,  by Elias M Stein and
Rami Shakarchi   published by Princeton University Press, and
Real Variables by Alberto Torchinsky published by Addison Wesley.

All 4 texts will be on 2-day reserve in the library.

Grades in the course will be based on solutions of homework problems and a final exam.
Every two weeks or so, I'll assign some  problems on the material covered.

My office hours are MW 2-3pm in my  office, PGH 696.

If you have any questions, call 713-743-3475 or send e-mail to auchmuty@uh.edu.
 

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