# Banach 27

This lecture (Banach27) was given on 10/28/09

### Excerpts

Defined the Fourier coeff. associated to a finite complex Borel measure on . The goal is to characterize for such measures. Recall an atom (in measure theory) is a set of positive measure that has not proper subset of positive measure.

Definitions

- Fourier coeff. of .
- positive definite and positive semidefinite sequences (This can be interpreted by looking at the principal minors of an infinite matrix)

Results

- Thm III.3.3 The seq is the seq of Fourier coeff. of a finite positive Borel measure on iff it is positive semidefinite.

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## About this entry

You’re currently reading “Banach 27,” an entry on Math Meandering

- Published:
- October 29, 2009 / 12:45 pm

- Category:
- Banach Algebras (Course)

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