MAGIC082: Banach spaces of analytic functions

Course details

Semester

Spring 2019
Monday, January 21st to Friday, March 29th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
40

Description

This course lies at the interface between complex analysis and operator theory. It will introduce the classical Hardy spaces, together with some of their cousins, and present the Toeplitz and Hankel operators defined on them. Applications to approximation and interpolation will be given.

Prerequisites

Familiarity with the main theorems of elementary complex analysis. Some experience of Hilbert spaces and the concept of a bounded linear operator. The definition, at least, of a Banach space.

Syllabus

This course will include most of the following:
1. Introduction. Examples of such spaces (Hardy spaces, Bergman spaces, Wiener algebra, Paley-Wiener space). (1)
2. Hardy spaces on the disc. Poisson kernel. Inner and outer functions. (5)
3. Operators on H2 and L2. Laurent, Toeplitz and Hankel operators. Nehari, Carathéodory-Fejér and Nevanlinna-Pick problems. Hilbert transform. (4)

Lecturer

  • JP

    Prof Jonathan Partington

    University
    University of Leeds

Bibliography

Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.

  • Banach spaces of analytic functions (K. Hoffman, )
  • Introduction to $H_p$ spaces (P. Koosis, )
  • Real and complex analysis (W. Rudin, )
  • Operators, functions and systems, an easy reading, Vol. 1. (N. Nikolskii, )

Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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