This is an arXiv category tag: it contains classical analysis (real analysis and harmonic analysis of Euclidean spaces), and ordinary differential equations as subjects.
Lie Groups
Some introductory notes about the definition and geometry of Lie groups, and their analysis.
The Translation Action on Function Spaces
Preliminaries Here's something I learned from Chongchun Zeng of Georgia Tech, while chatting over some hors-d'oeuvres at the AMS …
Some Periodic Functions
Some non-intuitive facts about periodic functions
An Elementary Proof of Young's Inequality
A proof of a generalized form of Young's inequality is given without the need of interpolation theory.
Joris' Theorem
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 …
Bessaga's converse to the contraction mapping theorem
A converse to Banach's fixed point theorem, due to Bessaga, is discussed.
Approximating Continuous Functions
Expository note on the Runge phenomenon
Notes on Sobolev Spaces
Lecture notes introducing Sobolev spaces.
Whitney Extension and Counterexample to Sard's Theorem
In a first course in differential geometry/topology we are often taught the following version of Sard's theorem: Theorem …
Mariş's Theorem
We describe a theorem due to Mihai Mariş concerning the symmetries of ground states.