There are no announcements




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.


Spring 2020 (Monday, January 20 to Friday, March 27)


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


  • Thu 12:05 - 12:55


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)

Other courses that you may be interested in:


Jonathan Partington
Phone (0113) 3435123
Photo of Jonathan Partington


Banach spaces of analytic functionsK. Hoffman
Introduction to $H_p$ spacesP. Koosis
Real and complex analysisW. Rudin
Operators, functions and systems, an easy reading, Vol. 1.N. Nikolskii


Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will 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.)


No assessment information is available yet.

No assignments have been set for this course.


No files have yet been uploaded for this course.

Recorded Lectures

Please log in to view lecture recordings.