Spectral Theory and Differential Operators by E. Brian Davies

Spectral Theory and Differential Operators



Download Spectral Theory and Differential Operators




Spectral Theory and Differential Operators E. Brian Davies
Language: English
Page: 188
Format: djvu
ISBN: 0521472504, 9780521472500
Publisher: Cambridge University Press

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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