Function Spaces and Partial Differential Equations: 2 Volume set

Function Spaces and Partial Differential Equations: 2 Volume set

by Ali Taheri


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This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.

Product Details

ISBN-13: 9780198733171
Publisher: Oxford University Press
Publication date: 10/01/2015
Series: Oxford Lecture Series in Mathematics and Its Applications
Pages: 496
Product dimensions: 6.30(w) x 9.50(h) x 2.10(d)

About the Author

Ali Taheri, Reader in Mathematics, University of Sussex

Dr Taheri is a reader in Mathematics as the University of Essex. His primary research area is in the field of Analysis & PDEs where he has been working for over 15 years. During which time he has published research papers in prestigious journals, made valuable contributions to the field and has taught and conducted research in some of the leading institutions in the world including Oxford, Courant Institute, Max-Planck-Institute Leipzig and Warwick. He heads up the Analysis and PDEs research group in Sussex with 11 faculty and 25 members. In June 2014 he was awarded the First University of Sussex Teaching Prize for "Outstanding and Innovative Postgraduate Teaching in Mathematics".

Table of Contents

1. Harmonic Functions and the Mean-Value Property
2. Poisson Kernels and Green's Representation Formula
3. Abel-Poisson and Fejer Means of Fourier Series
4. Convergence of Fourier Series: Dini vs. Dirichlet-Jordon
5. Harmonic-Hardy Spaces hp(D)
6. Interpolation Theorems of Marcinkiewicz and Riesz-Thorin
7. The Hilbert Transform on Lp(T) and Riesz's Theorem
8. Harmonic-Hardy Spaces hp(Bn)
9. Convolution Semigroups; The Poisson and Heat Kernels on Rn
10. Perron's Method of Sub-Harmonic Functions
11. From Abel-Poisson to Bochner-Riesz Summability
12. Fourier Transform on S'(Rn); The Hilbert-Sobolev spaces Hs(Rn)
13. Maximal Function; Bounding Averages and Pointwise Convergence
14. Harmonic-Hardy Spaces hp(H)
15. Sobolev Spaces; A Resolution of the Dirichlet Principle
16. Singular Integral Operators and Vector-Valued Inequalities
17. Littlewood-Paley Theory, Lp-Multipliers and Function Spaces
18. Morrey and Campanato vs. Hardy and John-Nirenberg Spaces
19. Layered Potentials, Jump Relations and Existence Theorems
20. Second Order Equations in Divergence Form: Continuous Coefficients
21. Second Order Equations in Divergence Form: Measurable Coefficients

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