### Abstract

This development formalises the square integrable functions over the reals and the basics of Fourier series. It culminates with a proof that every well-behaved periodic function can be approximated by a Fourier series. The material is ported from HOL Light: https://github.com/jrh13/hol-light/blob/master/100/fourier.ml

### License

BSD License

### Topics

- Mathematics/Analysis

### Session Fourier

- Periodic
- Lspace
- Square_Integrable
- Confine
- Fourier_Aux2
- Fourier

### Depends on

- Lp spaces

### Auto-related entries

- Pick’s Theorem
- Bertrand’s postulate
- The Cartan Fixed Point Theorems
- Basic Geometric Properties of Triangles

## Cite

×

Fourier-AFP

    @article{Fourier-AFP,
      author  = {Lawrence C. Paulson},
      title   = {Fourier Series},
      journal = {Archive of Formal Proofs},
      month   = {September},
      year    = {2019},
      note    = {\url{https://isa-afp.org/entries/Fourier.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

Download

## Download

× Download latest

Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
- Feb 23, 2021 : Isabelle2021
- Apr 18, 2020 : Isabelle2020
- Sep 11, 2019 : Isabelle2019