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HARMONIC ANALYSIS - 6 CFU

Teacher

Massimo Lanza De Cristoforis

Scheduled Period

I Year - 1 Semester | 04/10/2021 - 15/01/2022

Hours: 48 (16 esercitazione, 32 lezione)

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Prerequisites

Analysis courses of the first two years, and preferably the following courses

Real Analysis
Mathematical Methods
Functional Analysis 1

and the basic properties of harmonic functions, which will be anyway brushed up.

Target skills and knowledge

Theory of integal operators with singular and weakly singular kernel. Potential theory. Applications to boundary value problems for harmonic functions.

Examination methods

Partial tests and final oral exam

Assessment criteria

Evaluation of the knowledge of the candidate on each topic of the program

Course contents

Preliminaries on function spaces

Integral operators with weakly singular and singular kernel

Applications to the analysis of potentials

Elements of potential theory

Applications to boundary value problems for harmonic functions.

Planned learning activities and teaching methods

Theoretical exposition with exercises and examples

Additional notes about suggested reading

The course material is covered by hand-outs or references, which will be recommended.

Textbooks (and optional supplementary readings)

  • Lanza de Cristoforis, Massimo, Lectures on Distributions and Integral Operators, 2021 Dispense - Handouts
  • Dalla Riva, Matteo, Lanza de Cristoforis, Massimo, Musolino, Paolo, Singularly Perturbed Boundary Value Problems. A Functional Analytic Approach, 2021

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