## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- Instructional Workshop on Analysis and Geometry, Part 3. Tim Cranny and John Hutchinson, eds. Proceedings of the Centre for Mathematics and its Applications, v. 34. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1996), 35 - 76

### An introduction to some modern aspects of harmonic analysis

#### Abstract

The following notes were prepared as the text of a set of lectures given at the Workshop in Geometry and Analysis, held at the Australian National University in January 1995, and aimed at a mixed audience of postgraduate students and academics.

The aim of the lecture series was ambitious: in five hours to start from the level of undergraduate Fourier analysis and bring the participants to the point where they could take subsequent advanced lecture courses on Calder6n-Zygmund theory, semigroup theory, distributions etc.

I have sought to give an overview of what I see as the important parts of the theory. There are no proofs or examples to speak of, indications of some of these being provided in lectures. An exception is in Chapter 5, where I felt that the proof of Malgrange-Ehrenpreis nicely drew together the rest of the material.

The last chapter provides an introduction to noncommutative harmonic analysis.

#### Article information

**Dates**

First available in Project Euclid:
18 November 2014

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416323533

**Mathematical Reviews number (MathSciNet)**

MR1394695

**Zentralblatt MATH identifier**

0906.42001

#### Citation

Dooley, A. H. An introduction to some modern aspects of harmonic analysis. Instructional Workshop on Analysis and Geometry, Part 3, 35--76, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1996. https://projecteuclid.org/euclid.pcma/1416323533