Math 6320, Introduction to Real Analysis 2

Semester 2, 2018-19

Course Lecturer:

Dr. Judith Packer, Dept. of Mathematics

Tel: (303) 492-6979
Office: Math 227
Email: packer@euclid.colorado.edu
URL: http://math.colorado.edu/~packer

Course Information:
 This course is meant to continue the study of analysis of real-valued functions of one or several variables, with an emphasis on Lebesgue measure and Lebesgue integration on the real line and R^n. Topics to be covered include:
Functions of bounded variation on closed and bounded intervals in R, absolutely continuous functions, and the Fundamental Theorem of Calculus expressed using the Lebesgue integral. Locally compact Hausdorff spaces, the Stone-Weirstrass Theorem, the Arzela-Ascoli Theorem; Elements of functional analysis, including normed vector spaces, linear functionals, the Baire Category Theorem, Hilbert spaces; L^p - spaces, definitions and examples; Minkowski's inequality, Holder's inequality, interpolation of $L^p$-spaces; Radon measures: positive linear functionals on C_C(X) and the Riesz representation theorems, regularity of measures, the dual of $C_0(X),$ products of Radon measures; Elements of Fourier analysis: convolutions, the Fourier transform, summation of Fourier integrals and series and appplications of Hilbert space theory, pointwise convergence of Fourier series, Fourier analysis of measures.

Prerequisite:
 Math 6310, or instructor consent.

Course Text:
 We will use as a primary text the book "Real Analysis: Modern Techniques and their Applications", by G.B. Folland, covering most of Chapters 4 - 7, and part of Chapter 8.

Folland has an errata page for this textbook at http://www.math.washington.edu/~folland/Homepage/reals.pdf

Assessment: Lecture Hours and Venue:
MWF 2 p.m.-2:50 p.m. ECCR 139

Office Hours:
Mon. 4 p.m.=5 p.m., Wed., Fri. 3 p.m. - 4 p.m., and by appointment.

Homework:
Some Important Names associated with Real Analysis :

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Last modified January 12, 2019.