Function Spaces and Partial Differential Equations: Classical Analysis: Volume 1

ISBN : 9780198733133

Ali Taheri
528 ページ
163 x 236 mm
Oxford Lecture Series in Mathematics and Its Applications

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.


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 S0(Rn)
The Hilbert-Sobolev spaces Hs(Rn)


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 In June 2014 he was awarded the First University of Sussex Student Led Teaching Prize for Outstanding and Innovative Postgraduate Teaching in Mathematics.