# 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.

### 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.

### Where Does The π Go

It is fairly well known that experts in partial differential equations and experts in harmonic analysis prefer to define the Fourier …

### A Little Hilbert Space Problem

First let us consider the following question on a finite dimensional vector space. Let $(V, \langle\cdot\rangle)$ be a $k$-dimensional …