# Search results for: Yu. Kh. Èshkabilov

Theoretical and Mathematical Physics > 2016 > 186 > 2 > 268-279

*H*(

*ε*),

*ε*> 0. We prove that for a sufficiently small

*ε*> 0, this operator has no bound states and no two-particle branches of the spectrum. We also obtain an estimate for the small parameter

*ε*.

Siberian Advances in Mathematics > 2015 > 25 > 3 > 179-190

*H*. We also obtain an estimate for the number of eigenvalues below this boundary.

Lobachevskii Journal of Mathematics > 2013 > 34 > 3 > 256-263

*k*≥ 2. To study translation-invariant Gibbs measures of the model we drive an nonlinear functional equation. For

*k*= 2 and 3 under some conditions on parameters of the model we prove non-uniqueness of translation-invariant Gibbs measures (i.e., there are phase transitions).

Siberian Advances in Mathematics > 2013 > 23 > 4 > 227-233

Mathematical Physics, Analysis and Geometry > 2013 > 16 > 1 > 1-17

Siberian Advances in Mathematics > 2012 > 22 > 1 > 1-12

Theoretical and Mathematical Physics > 2010 > 164 > 1 > 896-904

Siberian Advances in Mathematics > 2009 > 19 > 3 > 151-161

*a, b*]

^{ ν }and let

*T*be a partially integral operator defined in

*L*

_{2}(Ω

^{2}) as follows: $$ (Tf)(x,y) = \int_\Omega {q(x,s,y)f(s,y)} d\mu (s). $$ In the article, we study the solvability of the partially integral Fredholm equations

*f*− ℵ

*Tf*=

*g*, where

*g*∈

*L*

_{2}(Ω

^{2}) is a given function and ℵ ∈ ℂ. The notion of determinant (which is a measurable function on Ω) is introduced for the operator

*E*−...

Siberian Advances in Mathematics > 2009 > 19 > 4 > 233-244

_{1}, Ω

_{2}⊂ ℝ

^{ν}be compact sets. In the Hilbert space

*L*

_{2}(Ω

_{1}× Ω

_{2}), we study the spectral properties of selfadjoint partially integral operators

*T*

_{1},

*T*

_{2}, and

*T*

_{1}+

*T*

_{2}, with $$ \begin{gathered} (T_1 f)(x,y) = \int_{\Omega _1 } {k_1 (x,s,y)f(s,y)d\mu (s),} \hfill \\ (T_2 f)(x,y) = \int_{\Omega _2 } {k_2 (x,t,y)f(x,t)d\mu (t),} \hfill \\ \end{gathered}...

Theoretical and Mathematical Physics > 2006 > 149 > 2 > 1497-1511

*L*

_{2}(

*T*

^{ ν }×

*T*

^{ ν }), where

*T*

^{ ν }is a

*ν*-dimensional torus, we study the spectral properties of the “three-particle” discrete Schrödinger operator Ĥ = H

_{0}+ H

_{1}+ H

_{2}, where H

_{0}is the operator of multiplication by a function and H

_{1}and H

_{2}are partial integral operators. We prove several theorems concerning the essential spectrum of Ĥ. We study the discrete and essential spectra of the Hamiltonians...