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Spectral Theory and Differential Operators book cover
Spectral Theory and Differential Operators
1995
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In this book, Davies introduces the reader to the theory of partial differential operators, up to the spectral theorem for bounded linear operators on Banach spaces. He also describes the theory of Fourier transforms and distributions as far as is needed to analyze the spectrum of any constant coefficient partial differential operator. He also presents a completely new proof of the spectral theorem for unbounded self-adjoint operators and demonstrates its application to a variety of second order elliptic differential operators. Finally, the book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. Illustrated with many examples, it is well-suited to graduate-level work.
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Author

E Brian Davies
E Brian Davies
Author · 4 books

E. Brian Davies was awarded a first class degree in Mathematics at the University of Oxford in 1965 and a D Phil., also at Oxford, in 1968, when he was also awarded the Senior Mathematical Prize. After two years in the USA, at Princeton and MIT, he took up a permanent position as a Tutorial Fellow at St John’s College, Oxford. From 1973 he was a University Lecturer at the University of Oxford. In 1981 Davies was appointed as Professor of Mathematics at King's College, London, where he remained until his official retirement in 2010. He was Head of Department between 1990 and 1993. He was the founding Editor of the London Mathematical Society Student Texts between 1983 and 1990, and the founding Editor of the Journal of Spectral Theory, published by the European Mathematical Society, from 2010. In March 1995 Davies was elected a Fellow of the Royal Society, in recognition of his seminal work in spectral theory and particularly on the heat kernels of diffusion equations, of great relevance in quantum theory and other fields. In June 1996 he was elected a Fellow of King's College, London. In June 1998 he was awarded the Senior Berwick Prize by the London Mathematical Society. He was President of the London Mathematical Society in 2008 and 2009. As well as over two hundred research papers, Davies has published five monographs and two popular books on the philosophy of mathematics and science.

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