Representation Theorems in Hardy Spaces

Javad Mashreghi (Université Laval, Québec)

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English

Cambridge University Press
19 March 2009

Calculus & mathematical analysis; Complex analysis, complex variables

Series: London Mathematical Society Student Texts

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.

By: Javad Mashreghi (Université Laval Québec)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 74
Dimensions: Height: 234mm, Width: 157mm, Spine: 24mm
Weight: 660g
ISBN: 9780521517683
ISBN 10: 0521517680
Series: London Mathematical Society Student Texts
Pages: 384
Publication Date: 19 March 2009
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

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.

Reviews for Representation Theorems in Hardy Spaces

Mathematicians working on related topics should find it a useful reference for statements and proofs of many of the classical results related the the Hardy spaces. Anyone teaching a course that includes Hardy spaces would find it a good source for homework problems. Peter Rosenthal, CMS Notes ... self-contained and clearly written text... The main strength of this book is a large number of exercises (over 300), which makes it a good textbook choice. Marcin M. Bownik, Mathematical Reviews