The 245B final can be found here.  I am not posting solutions, but readers (both students and non-students) are welcome to discuss the final questions in the comments below.

The continuation to this course, 245C, will begin on Monday, March 29.  The topics for this course are still somewhat fluid – but I tentatively plan to cover the following topics, roughly in order:

• $L^p$ spaces and interpolation; fractional integration
• The Fourier transform on ${\Bbb R}^n$ (a very quick review; this is of course covered more fully in 247A)
• Schwartz functions, and the theory of distributions
• Hausdorff measure
• The spectral theorem (introduction only; the topic is covered in depth in 255A)

I am open to further suggestions for topics that would build upon the 245AB material, which would be of interest to students, and which would not overlap too substantially with other graduate courses offered at UCLA.