Representation Theorems in Hardy Spaces

Erscheinungsjahr 2009
ISBN: 978-0-521-73201-7
Verlag: Cambridge University Press

Buch, Englisch, Band 74, 384 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 558 g

Reihe: 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.

Autoren/Hrsg.

Mashreghi, Javad

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.

Über Autor(innen)

Mashreghi, Javad
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.