Výsledky vyhledávání - "Safarov, Yuri"

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Distance to normal elements in $C^*$-algebras of real rank zero

We obtain an order sharp estimate for the distance from a given bounded operator $A$ on a Hilbert space to the set of normal operators in terms of $\|[A,A^*]\|$ and the distance to the set of invertible operators. A slightly modified estimate holds i

Externí odkaz: http://arxiv.org/abs/1403.2021

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Lower bounds for the counting function of integral operators

Autor: Safarov, Yuri

Publikováno v: Operator Theory: Advances and Applications, Vol. 228 (2013), pp. 343-354

The paper presents a lower bound for the number of negative eigenvalues of an integral operator with continuous kernel K lying below a nonpositive number t. The estimate is given in terms of some integrals of K.

Externí odkaz: http://arxiv.org/abs/1308.4078

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A symbolic calculus for Fourier integral operators

Autor: Safarov, Yuri

The paper develops a symbolic calculus for Fourier integral operators associated with canonical transformations.
Comment: To appear in the CRM conference proceeding series

Externí odkaz: http://arxiv.org/abs/1308.4073

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The semiclassical theory of discontinuous systems and ray-splitting billiards

Autor: Jakobson, Dmitry, Safarov, Yuri, Strohmaier, Alexander, de Verdiere, Yves Colin

Publikováno v: American Journal of Mathematics, Volume 137, Number 4, August 2015, pp. 859-906

We analyze the semiclassical limit of spectral theory on manifolds whose metrics have jump-like discontinuities. Such systems are quite different from manifolds with smooth Riemannian metrics because the semiclassical limit does not relate to a class

Externí odkaz: http://arxiv.org/abs/1301.6783

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Average growth of the spectral function on a Riemannian manifold

Autor: Lapointe, Hugues, Polterovich, Iosif, Safarov, Yuri

We study average growth of the spectral function of the Laplacian on a Riemannian manifold. Two types of averaging are considered: with respect to the spectral parameter and with respect to a point on a manifold. We obtain as well related estimates o

Externí odkaz: http://arxiv.org/abs/0803.4171

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Birkhoff's theorem and multidimensional numerical range

Autor: Safarov, Yuri

Publikováno v: J. Funct. Anal., Vol. 222, 1 (2005), 61--97

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.

Externí odkaz: http://arxiv.org/abs/math/0110131

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