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Representation Theorems in Hardy Spaces

Part of London Mathematical Society Student Texts

Author: Javad Mashreghi, Université Laval, Québec

Date Published: No date available
availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
format: Adobe eBook Reader
isbn: 9781107299238

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About the Authors

The theory of Hardy spaces has close connections to many branches of mathematics including Fourier analysis, harmonic analysis, singular integrals, potential theory and operator theory, and has found essential applications in robust control engineering. For each application, the ability to represent elements of these classes by series or integral formulas is of utmost importance. This self-contained text provides an introduction to a wide range of representation theorems and provides a complete description of the representation theorems with direct proofs for both classes of Hardy spaces: Hardy spaces of the open unit disc and Hardy spaces of the upper half plane. With over 300 exercises, many with accompanying hints, this book is ideal for those studying Advanced Complex Analysis, Function Theory or Theory of Hardy Spaces. Advanced undergraduate and graduate students will find the book easy to follow, with a logical progression from basic theory to advanced research.
- Concise and accessible, provides complete description of representation theorems with direct proofs for both classes of Hardy spaces
- Contains over 300 exercises, many with accompanying hints, to aid understanding
- Ideal for advanced undergraduate and graduate students taking courses in Advanced Complex Analysis, Function Theory or Theory of Hardy Spaces
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Product details
- format: Adobe eBook Reader
- isbn: 9781107299238
- contains: 16 b/w illus. 2 tables 335 exercises
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
Preface
1. Fourier series
2. Abel–Poisson means
3. Harmonic functions in the unit disc
4. Logarithmic convexity
5. Analytic functions in the unit disc
6. Norm inequalities for the conjugate function
7. Blaschke products and their applications
8. Interpolating linear operators
9. The Fourier transform
10. Poisson integrals
11. Harmonic functions in the upper half plane
12. The Plancherel transform
13. Analytic functions in the upper half plane
14. The Hilbert transform on R
A. Topics from real analysis
B. A panoramic view of the representation theorems
Bibliography
Index.
Author
Javad Mashreghi, Université Laval, Québec
Professor Javad Mashreghi is Bonyan Research Chair in Mathematical Analysis in the Department of Mathematics and Statistics at Laval University, Quebec. He won the prestigious G. de B. Robinson Award of the Canadian Mathematical Society in 2004 for two long research papers published in the Canadian Journal of Mathematics. His research interests are complex and harmonic analysis and their applications in applied sciences.