Advanced Topics in Complex Analysis
A.Y. 2018/2019
Learning objectives
Introduction to the more known spaces of holomorphic functions in the disc and in a half plane. Analysis of their properties, with attention to the proofs techniques. The focus is on Hardy and (weighted) Bergman spaces on the disc and in a half plane, Paley-Wiener spaces and Bernstein spaces.
Expected learning outcomes
Knowledge of the topics and results, and application to exercises that need also computational techniques.
Lesson period: Second semester
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Hardy spaces Hp(D) on the unit disc.
Function spaces with reproducing kernel.
Bergman spaces Ap(D) and weighted Bergman spaces Aνp(D).
Lp boundedness of the Bergman and Cauchy-Szego projections.
Fourier tranform on R of the spaces L1 and L2.
Paley—Wiener theorems.
Bergman and Hardy spaces in the upper half plane.
Introduction to several complex variables theory.
Holomorphic fuctions on the unit disc, Hardy and Bergman spaces, projections and boundedness in Lp.
Function spaces with reproducing kernel.
Bergman spaces Ap(D) and weighted Bergman spaces Aνp(D).
Lp boundedness of the Bergman and Cauchy-Szego projections.
Fourier tranform on R of the spaces L1 and L2.
Paley—Wiener theorems.
Bergman and Hardy spaces in the upper half plane.
Introduction to several complex variables theory.
Holomorphic fuctions on the unit disc, Hardy and Bergman spaces, projections and boundedness in Lp.
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 6
Lessons: 42 hours
Professor:
Peloso Marco Maria
Educational website(s)
Professor(s)
Reception:
By appointment
My office, room 1021 Dipartimento di Matematica