Representation Theorems in Hardy Spaces
Representation Theorems in Hardy Spaces
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
Reviews & endorsements
"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
Product details
No date availableAdobe eBook Reader
9781107299238
0 pages
0kg
16 b/w illus. 2 tables 335 exercises
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.
