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.

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.

In a first course in differential geometry/topology we are often taught the following version of Sard's theorem: Theorem …

We describe a theorem due to Mihai Mariş concerning the symmetries of ground states.

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

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