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General


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.

Semester

Spring 2018 (Monday, January 22 to Friday, March 16; Monday, April 23 to Friday, May 4)

Timetable

  • Fri 11:05 - 11:55

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


Jonathan Partington
Email j.r.partington@leeds.ac.uk
Phone (0113) 3435123
Photo of Jonathan Partington


Students


Photo of Dimitris Chiotis
Dimitris Chiotis
(Newcastle)


Bibliography


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


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Assessment



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Recorded Lectures


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