Function Spaces and Partial Differential Equations: 2 Volume set

Paperback | August 30, 2015

byAli 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 bookprimarily 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 bythe 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.

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From the Publisher

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 bookprimarily lies in its clear and detailed explan...

Dr Taheri is a Reader in Mathematics as the University of Sussex. His primary research area is in the field of Analysis and 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...

other books by Ali Taheri

Format:PaperbackDimensions:992 pages, 9.21 × 6.14 × 2.24 inPublished:August 30, 2015Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198733178

ISBN - 13:9780198733171

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Table of Contents

1. Harmonic Functions and the Mean-Value Property2. Poisson Kernels and Green's Representation Formula3. Abel-Poisson and Fejer Means of Fourier Series4. Convergence of Fourier Series: Dini vs. Dirichlet-Jordon5. Harmonic-Hardy Spaces hp(D)6. Interpolation Theorems of Marcinkiewicz and Riesz-Thorin7. The Hilbert Transform on Lp(T) and Riesz's Theorem8. Harmonic-Hardy Spaces hp(Bn)9. Convolution Semigroups; The Poisson and Heat Kernels on Rn10. Perron's Method of Sub-Harmonic Functions11. From Abel-Poisson to Bochner-Riesz Summability12. Fourier Transform on S'(Rn); The Hilbert-Sobolev spaces Hs(Rn)13. Maximal Function; Bounding Averages and Pointwise Convergence14. Harmonic-Hardy Spaces hp(H)15. Sobolev Spaces; A Resolution of the Dirichlet Principle16. Singular Integral Operators and Vector-Valued Inequalities17. Littlewood-Paley Theory, Lp-Multipliers and Function Spaces18. Morrey and Campanato vs. Hardy and John-Nirenberg Spaces19. Layered Potentials, Jump Relations and Existence Theorems20. Second Order Equations in Divergence Form: Continuous Coefficients21. Second Order Equations in Divergence Form: Measurable Coefficients