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Search Results: 1 - 10 of 512875 matches for " A. I. Nazarov "
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Exact L_2-small ball asymptotics of Gaussian processes and the spectrum of boundary value problems with "non-separated" boundary conditions
A. I. Nazarov
Mathematics , 2007,
Abstract: We sharpen a classical result on the spectral asymptotics of the boundary value problems for self-adjoint ordinary differential operator. Using this result we obtain the exact $L_2$-small ball asymptotics for a new class of zero mean Gaussian processes. This class includes, in particular, integrated generalized Slepian process, integrated centered Wiener process and integrated centered Brownian bridge.
On a set of transformations of Gaussian random functions
A. I. Nazarov
Mathematics , 2008,
Abstract: We consider a set of one-dimensional transformations of Gaussian random functions. Under natural assumptions we obtain a connection between $L_2$-small ball asymptotics of the transformed function and of the original one. Also the explicit Karhunen -- Lo\'eve expansion is obtained for a proper class of Gaussian processes.
Log-Level Comparison Principle for Small Ball Probabilities
A. I. Nazarov
Mathematics , 2008,
Abstract: We prove a new variant of comparison principle for logarithmic $L_2$-small ball probabilities of Gaussian processes. As an application, we obtain logarithmic small ball asymptotics for some well-known processes with smooth covariances.
On the maximum principle for parabolic equations with unbounded coefficients
A. I. Nazarov
Mathematics , 2015,
Abstract: Translation of the paper "Interpolation of linear spaces and maximum estimates for solutions to parabolic equations" published in Russian in the collected volume "Partial differential equations", Akad. Nauk SSSR, Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1987, 50--72. Original proofs are essentially simplified. Some gaps are fixed and some comments are added.
Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes
A. I. Nazarov,I. A. Sheipak
Mathematics , 2010, DOI: 10.1112/blms/bdr056
Abstract: We find the logarithmic small ball asymptotics for the $L_2$-norm with respect to a degenerate self-similar measures of a certain class of Gaussian processes including Brownian motion, Ornstein - Uhlenbeck process and their integrated counterparts.
The Dirichlet Problem for Non-divergence Parabolic Equations with Discontinuous in Time Coefficients
V. A. Kozlov,A. I. Nazarov
Mathematics , 2009,
Abstract: We establish pointwise estimates for the Green function to the Dirichlet problem for parabolic equation with coefficients measurable in time variable. Using these estimate we obtain coercive estimates for this problem in anisotropic weighted Lebesgue spaces and prove the solvability theorems.
On symmetry of extremals in several embedding theorems
E. V. Mukoseeva,A. I. Nazarov
Mathematics , 2014,
Abstract: We study the symmetry/asymmetry of functions providing sharp constants in the embedding theorems ${\stackrel{\circ}{W}}\vphantom{W}_2^r(-1,1)\hookrightarrow{\stackrel{\circ}{W}}\vphantom{W}_\infty^k(-1,1)$ for various $r$ and $k$. The sharp constants for all $r>k$ in the cases $k=4$ and $k=6$ are calculated explicitly as well.
On S.L. Tabachnikov's conjecture
A. I. Nazarov,F. V. Petrov
Mathematics , 2005,
Abstract: S. L. Tabachnikov's conjecture is proved: for any closed curve $\Gamma$ lying inside convex closed curve $\Gamma_1$ the mean absolute curvature $T(\Gamma)$ exceeds $T(\Gamma_1)$ if $\Gamma\ne k\Gamma_1$. An inequality $T(\Gamma)\ge T(\Gamma_1)$ is proved for curves in a hemisphere.
On monotonicity of some functionals under rearrangements
S. V. Bankevich,A. I. Nazarov
Mathematics , 2014,
Abstract: We consider the Polya--Szeg\"o type weighted inequality. We prove this inequality for monotone rearrangement and for Steiner's symmetrization.
A counterexample to the Hopf-Oleinik lemma (elliptic case)
D. E. Apushkinskaya,A. I. Nazarov
Mathematics , 2015,
Abstract: We construct a new counterexample confirming the sharpness of the Dini-type condition for the boundary of $\Omega$. In particular, we show that for convex domains the Dini-type assumption is the necessary and sufficient condition which guarantees the Hopf-Oleinik type estimates.
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