Hi. I want to get a quick overview of the theory of Hilbert spaces in order to understand fourier series and transforms at a higher level. I have a couple of questions I hoped someone could help me with.(adsbygoogle = window.adsbygoogle || []).push({});

- First of all: Can anyone recommend any literature, notes etc.. which go through the sufficient results of Hilbert and Banach spaces (in a quick way) with the aim to understand Fourier theory?

-What is the virtue of a Hilbert space being defined as a Banach space, i.e. a normed linear space in which any Cauchy sequence of elements converge to an element in the space?

- How do I prove that ##L^2 (S^1)## where ##S^1## is the circle is a Banach space with the standard hilbert space norm

$$\langle f, g\rangle = \int_{S^1} f^*(x) g(x) dx?$$

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Hilbert, Banach and Fourier theory

Loading...

Similar Threads - Hilbert Banach Fourier | Date |
---|---|

I Understanding Hilbert Vector Spaces | Mar 2, 2018 |

I Can we construct a Lie algebra from the squares of SU(1,1) | Feb 24, 2018 |

I Question about inverse operators differential operators | Feb 9, 2018 |

A What separates Hilbert space from other spaces? | Jan 15, 2018 |

Projections on Banach and Hilbert spaces | Oct 4, 2007 |

**Physics Forums - The Fusion of Science and Community**