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Your search keyword '"Yuri Safarov"' showing total 4 results
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4 results on '"Yuri Safarov"'

1. Pseudodifferential operators on manifolds: a coordinate-free approach

Author

Yuri Safarov and Peter McKeag

Subjects
Semi-elliptic operator, Elliptic operator, Coordinate-free, Parametrix, Laplace–Beltrami operator, Local coordinates, Calculus, Operator theory, Mathematics, Quasinormal operator
Abstract

The main aim of the paper is to demonstrate the advantage of a coordinate-free approach to the theory of pseudodifferential operators. We explain how one can define symbols and construct a symbolic calculus without using local coordinates, briefly review some known definitions and results, and discuss possible applications and further developments.

Published
2011

2. Birkhoff's theorem and multidimensional numerical range

Author

Yuri Safarov

Subjects
47A12, 05C50, Pure mathematics, Extreme points, Variational principle, Operator (physics), Spectrum (functional analysis), Mathematical analysis, Convex set, Mathematics::Spectral Theory, Mathematics - Spectral Theory, FOS: Mathematics, Countable set, Weighted graphs, Birkhoff's theorem, Extreme point, Numerical range, Spectral Theory (math.SP), Analysis, Eigenvalues and eigenvectors, Mathematics, Stochastic matrices
Abstract

We study the relation between the spectrum of a self-adjoint operator and its multidimensional numerical range. It turns out that the multidimensional numerical range is a convex set whose extreme points are sequences of eigenvalues of the operator. Every collection of eigenvalues which can be obtained by the Rayleigh--Ritz formula generates an extreme point of the multidimensional numerical range. However, it may also have other extreme points., 35 pages

Published
2001

3. Spectral Theory and Geometry

Author

E. Brian Davies, Yuri Safarov, E. Brian Davies, and Yuri Safarov

Subjects
Geometry, Differential--Congresses, Riemannian manifolds--Congresses, Spectral geometry--Congresses, Spectral theory (Mathematics)--Congresses
Abstract

This volume brings together lectures from an instructional meeting on spectral theory and geometry held under the auspices of the International Centre for Mathematical Sciences in Edinburgh. The contributions here come from world experts and many are much expanded versions of the lectures they gave. Together they survey the core material and go beyond to reach deeper results. For graduate students and experts alike, this book will be a highly useful resource.

Published
1999

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