math.CA

This is an arXiv category tag: it contains classical analysis (real analysis and harmonic analysis of Euclidean spaces), and ordinary differential equations as subjects.

The goal of this post is to make sense of the notion of the "product integral". Typically this is described with the analogy: …
9 min read Expository

I was surprised to learn that in some ways the discrete Schrodinger equation is very different from the its continuum cousin.
Last updated on 6 min read mathematical diversions

A narration of the problem solving process.
Last updated on 11 min read mathematical diversions

A fundamental result in measure theory is Egorov's Theorem, which says that if a sequence of measurable functions converge point-wise, …
Last updated on 11 min read mathematical diversions

Apologies if this post is shoddily written; I mainly just wanted to record an explicit counterexample before I forget it, and this post …
Last updated on 4 min read Mathematical diversions

Embedding theorems for Weighted Sobolev Spaces
Last updated on 8 min read Expository

This post concerns the second mean value theorem for definite integrals. Theorem    [Second MVT for Integrals] Let $w$ be a …
Last updated on 4 min read expository

Since I am preparing to teach intro real analysis this fall, it is a good time for me to get reacquainted with Riemann integration and …
Last updated on 8 min read expository

This short post aims at proving a general version of the Moore-Osgood Theorem on interchanging of limits. Theorem   …
Last updated on 2 min read expository

L. Craig Evans is a professor at UC Berkeley. For many students he is best known for his textbook on partial differential equations. I …
Last updated on 10 min read notes from talks