MAGIC082: Banach spaces of analytic functions

Course details


Spring 2014
Monday, January 20th to Friday, March 28th


Live lecture hours
Recorded lecture hours
Total advised study hours


11:05 - 11:55


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.


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.


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)


  • JP

    Prof Jonathan Partington

    University of Leeds


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, )



The assessment for this course will be via a single take-home paper at the end and with 2 weeks to complete and submit online. There will be 5 questions and you will need to do the equivalent of 2.5 questions to pass.

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