Function Spaces and Partial Differential Equations
Volume 1 - Classical Analysis
Series: Oxford Lecture Series in Mathematics and Its Applications;
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Product details:
- Publisher OUP Oxford
- Date of Publication 30 July 2015
- ISBN 9780198733133
- Binding Hardback
- No. of pages528 pages
- Size 236x163x30 mm
- Weight 960 g
- Language English 0
Categories
Short 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.
MoreLong 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.
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.
Table of Contents:
Harmonic Functions and the Mean-Value Property
Poisson Kernels and Green's Representation Formula
Abel-Poisson and Fejer Means of Fourier Series
Convergence of Fourier Series: Dini vs. Dirichlet-Jordon
Harmonic-Hardy Spaces hp(D)
Interpolation Theorems of Marcinkiewicz and Riesz-Thorin
The Hilbert Transform on Lp(T) and Riesz's Theorem
Harmonic-Hardy Spaces hp(Bn)
Convolution Semigroups; The Poisson and Heat Kernels on Rn
Perron's Method of Sub-Harmonic Functions
From Abel-Poisson to Bochner-Riesz Summability
Fourier Transform on S0(Rn); The Hilbert-Sobolev spaces Hs(Rn)
