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Search Results: 1 - 10 of 289985 matches for " E B Davies "
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The Role of Astronomy in the History of Science
E B Davies
Physics , 2002,
Abstract: We discuss the extent to which the visibility of the heavens was a necessary condition for the development of science, with particular reference to the measurement of time. Our conclusion is that while astronomy had significant importance, the growth of most areas of science was more heavily influenced by the accuracy of scientific instruments, and hence by current technology.
Spectral Properties of Random Non-self-adjoint Matrices and Operators
E B Davies
Physics , 2000,
Abstract: We describe some numerical experiments which determine the degree of spectral instability of medium size randomly generated matrices which are far from self-adjoint. The conclusion is that the eigenvalues are likely to be intrinsically uncomputable for similar matrices of a larger size. We also describe a stochastic family of bounded operators in infinite dimensions for almost all of which the eigenvectors generate a dense linear subspace, but the eigenvalues do not determine the spectrum. Our results imply that the spectrum of the non-self-adjoint Anderson model changes suddenly as one passes to the infinite volume limit.
Sharp boundary estimates for elliptic operators
E B Davies
Physics , 1998,
Abstract: We prove sharp L^2 boundary decay estimates for the eigenfunctions of certain second order elliptic operators acting in a bounded region, and of their first order space derivatives, using only the Hardy inequality. We then deduce bounds on the change of the eigenvalues when the region is reduced slightly in size, subject to DBCs.
A review of Hardy inequalities
E B Davies
Physics , 1998,
Abstract: We review the literature concerning the Hardy inequality for regions in Euclidean space and in manifolds, concentrating on the best constants. We also give applications of these inequalities to boundary decay and spectral approximation.
Spectral Theory of Pseudo-Ergodic Operators
E. B. Davies
Physics , 2000, DOI: 10.1007/s002200000352
Abstract: We define a class of pseudo-ergodic non-self-adjoint Schr\"odinger operators acting in spaces $l^2(X)$ and prove some general theorems about their spectral properties. We then apply these to study the spectrum of a non-self-adjoint Anderson model acting on $l^2(\Z)$, and find the precise condition for 0 to lie in the spectrum of the operator. We also introduce the notion of localized spectrum for such operators.
Semi-classical Analysis and Pseudospectra
E. B. Davies
Mathematics , 2004,
Abstract: We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also investigate the connections between pseudospectra and boundary conditions in the semi-classical limit.
Triviality of the Peripheral Point Spectrum
E. B. Davies
Mathematics , 2005,
Abstract: If $T_t=\rme^{Zt}$ is a positive one-parameter contraction semigroup acting on $l^p(X)$ where $X$ is a countable set and $1\leq p <\infty$, then the peripheral point spectrum $P$ of $Z$ cannot contain any non-zero elements. The same holds for Feller semigroups acting on $L^p(X)$ if $X$ is locally compact.
Algebraic aspects of spectral theory
E. B. Davies
Mathematics , 2010, DOI: 10.1112/S0025579310001579
Abstract: We describe some aspects of spectral theory that involve algebraic considerations but need no analysis. Some of the important applications of the results are to the algebra of $n\times n$ matrices with entries that are polynomials or more general analytic functions.
An Inverse Spectral Theorem
E. B. Davies
Mathematics , 2010,
Abstract: We prove a substantial extension of an inverse spectral theorem of Ambarzumyan, and show that it can be applied to arbitrary compact Riemannian manifolds, compact quantum graphs and finite combinatorial graphs, subject to the imposition of Neumann (or Kirchhoff) boundary conditions.
Archimedes' calculations of square roots
E. B. Davies
Mathematics , 2011,
Abstract: We reconsider Archimedes' evaluations of several square roots in 'Measurement of a Circle'. We show that several methods proposed over the last century or so for his evaluations fail one or more criteria of plausibility. We also provide internal evidence that he probably used an interpolation technique. The conclusions are relevant to the precise calculations by which he obtained upper and lower bounds on pi.
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