# Banach Lecture 8

This lecture (banach8) was given on 9/14/09.

### Excerpts

This lecture presented many examples of Gelfond Theory.

1. Consider again . It was shown can be identified with . Writing as it follows that

conclusion: is a function on the unit circle with absolutely convergent Fourier series. An so define the Weiner Algebra

it become a banach algebra.

Thm I.8.1 (D.Levy) Let and holom. on open set containing , then .

proof: apply thm I.7.2.

Cor. (N Weiner) If , then .

Rmk: this is hard result to prove without Gelfond theory.

Some more examples included determining for equal

- the Disk algebra = , norm is sup norm.

Thm. I.8.2 Let have no common zero in the closed unit disk. Then there exists s.t .

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You’re currently reading “Banach Lecture 8,” an entry on Math Meandering

- Published:
- September 15, 2009 / 2:09 pm

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- Banach Algebras (Course)

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