Basic Info

• Lectures: MWF 11-12, BA6183
• Office hours: Monday 12-1, Friday 12-1.
• TA: David Pechersky
• Textbook: Gerald Folland, Real Analysis Modern Techniques and Their Applications 2e
• Course Website: Quercus

Topics

• Hilbert spaces: orthogonal projections, orthonormal bases, Bessel’s inequality, parseval’s identity, operators in Hilbert spaces, spectral theorem for compact operators
• Topics in functional analysis, supplementing those covered in part I.
• Inequalities in Lp spaces, weak Lp spaces, interpolation theorems
• Fourier series and Fourier transform
• Distributions: Test functions, weak derivatives, Schwartz spaces, Sobolev spaces
• Some spectral theory of compact operators in Banach spaces
• Select additional topics if time allows.

References

• Functional analysis:

  • John B Conway, A course in Functional Analysis
  • Walter Rudin, Functional Analysis, 2e.

• Real analysis:

  • Barry Simon, Real Analysis, A comprehensive course in Analysis, Part 1.
  • Elias Stein and Rami Sharkarchi, Princeton Lectures in Analysis, volume 1, Fourier Analysis and volume 3, Real Analysis

  We may also consult other sources that will be mentioned later.

Evaluation

• Homework 30%: Weekly, due Wednesdays in class.
• Midterm Test 30%: Friday February 15, time and place TBA.
• Final Exam 40%. Time and place TBA.