Representation Theorems in Hardy Spaces 1st Edition by Javad Mashreghi ISBN 0521732018 9780521732017

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Product details:

ISBN 10: 0521732018

ISBN 13: 9780521732017 

Author: Javad Mashreghi

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

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.

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Tags: Javad Mashreghi, Representation Theorems, Hardy Spaces