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

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

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

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

Lecture notes introducing Sobolev spaces.