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pro vyhledávání: '"Kordyukov, A."'
We consider the Schr\"odinger operator $H(\mu) = \nabla_{\bf A}^*\nabla_{\bf A} + \mu V$ on a Riemannian manifold $M$ of bounded geometry, where $\mu>0$ is a coupling parameter, the magnetic field ${\bf B}=d{\bf A}$ and the electric potential $V$ are
Externí odkaz:
http://arxiv.org/abs/2412.17746
Autor:
Kordyukov, Yuri A.
We study asymptotic spectral properties of the Bochner-Schr\"odinger operator $H_{p}=\frac 1p\Delta^{L^p\otimes E}+V$ on high tensor powers of a Hermitian line bundle $L$ twisted by a Hermitian vector bundle $E$ on a Riemannian manifold $X$ of bounde
Externí odkaz:
http://arxiv.org/abs/2404.19684
Let $F$ be a transversely oriented foliation of codimension 1 on a closed manifold $M$, and let $\phi=\{\phi^t\}$ be a foliated flow on $(M,F)$. Assume the closed orbits of $\phi$ are simple and its preserved leaves are transversely simple. In this c
Externí odkaz:
http://arxiv.org/abs/2402.06671
We treat the notion of principal symbol mapping on a compact smooth manifold as a $\ast$-homomorphism of $C^{\ast}$-algebras. Principal symbol mapping is built from the ground, without referring to the pseudodifferential calculus on the manifold. Our
Externí odkaz:
http://arxiv.org/abs/2309.04500
Autor:
Kordyukov, Y. A., Taimanov, I. A.
Publikováno v:
Math. Notes 114:6 (2023), 1277-1288
Using the generalization of the multidimensional WKB method to magnetic Laplacians corresponding to monopoles, which we proposed earlier, we obtain explicit formulas for quasi-classical approximations of eigenfunctions for the Dirac monopole.
Co
Co
Externí odkaz:
http://arxiv.org/abs/2308.03731
Given a closed manifold $M$ and a closed regular submanifold $L$, consider the corresponding locally convex space $I=I(M,L)$ of conormal distributions, with its natural topology, and the strong dual $I'=I'(M,L)=I(M,L;\Omega)'$ of the space of conorma
Externí odkaz:
http://arxiv.org/abs/2304.00798
Autor:
Kordyukov, Yu., Manuilov, V.
Recently, M. Ludewig and G. C. Thiang introduced a notion of a uniformly localized Wannier basis with localization centers in an arbitrary uniformly discrete subset $D$ in a complete Riemannian manifold $X$. They show that, under certain geometric co
Externí odkaz:
http://arxiv.org/abs/2304.00125
Autor:
Kordyukov, Yuri A.
The paper is devoted to the trace formula for the magnetic Laplacian associated with a magnetic system on a compact manifold. This formula is a natural generalization of the semiclassical Gutzwiller trace formula and reduces to it in the case when th
Externí odkaz:
http://arxiv.org/abs/2208.04599
Autor:
Kordyukov, Yuri A.
The Bochner-Schr\"odinger operator $H_{p}=\frac 1p\Delta^{L^p\otimes E}+V$ on tensor powers $L^p$ of a Hermitian line bundle $L$ twisted by a Hermitian vector bundle $E$ on a Riemannian manifold of bounded geometry is studied. For any function $\varp
Externí odkaz:
http://arxiv.org/abs/2205.09011
Publikováno v:
Regular and Chaotic Dynamics, 2022, vol. 27, no. 4, pp. 460-476
We compute the trace formula for the magnetic Laplacian on a compact hyperbolic surface of constant curvature with constant magnetic field for energies above the Mane critical level of the corresponding magnetic geodesic flow. We discuss the asymptot
Externí odkaz:
http://arxiv.org/abs/2202.06055