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

L. Craig Evans is a professor at UC Berkeley. For many students he is best known for his textbook on partial differential equations. I …

When does a polynomial with real coefficients have only real roots? Here's one way to determine it.

A follow up to my previous post on Young's inequality.

Some introductory notes about the definition and geometry of Lie groups, and their analysis.

Preliminaries Here's something I learned from Chongchun Zeng of Georgia Tech, while chatting over some hors-d'oeuvres at the AMS …

Some non-intuitive facts about periodic functions

A proof of a generalized form of Young's inequality is given without the need of interpolation theory.

A proof is given of Joris' theorem, which states that if two coprime powers of a function are both smooth, then so is the original …

A converse to Banach's fixed point theorem, due to Bessaga, is discussed.

Expository note on the Runge phenomenon