Function Spaces and Partial Differential Equations
2 Volume set
Published on 30. July 2015
Other
Multiple copy pack
1030 pages
978-0-19-873317-1 (ISBN)
Description
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.
Reviews / Votes
The book is clearly written and is a valuable addition to the literature. It is warmly recommended to the graduate student. For the instructor, it is an excellent resource for graduate courses and seminars in analysis and partial differential equations. * Valentin Keyantuo, MathSciNet *More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Target group
College/higher education
Illustrations
22
Dimensions
Height: 240 mm
Width: 165 mm
Thickness: 57 mm
Weight
2 gr
ISBN-13
978-0-19-873317-1 (9780198733171)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
07/2015
Oxford University Press
€187.00
Shipment within 15-20 days
Person
Dr Taheri is a Reader in Mathematics as the University of Sussex. 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 Student Led Teaching Prize for "Outstanding and Innovative Postgraduate Teaching in Mathematics".
Content
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