# Search results for: A. K. Motovilov

Functional Analysis and Its Applications > 2019 > 53 > 3 > 192-204

*T*be a self-adjoint operator on a Hilbert space

*H*with domain $$\mathscr{D}(T)$$ D ( T ) . Assume that the spectrum of

*T*is contained in the union of disjoint intervals Δ

_{k}= [

*α*

_{2k−1},

*α*

_{2k}],

*k*∈ ℤ, the lengths of the gaps between which satisfy the inequalities $${\alpha _{2k + 1}} - {\alpha _{2k}}\geqslant b{\rm{|}}{\alpha _{2k + 1}} + {\alpha _{2k}}{{\rm{|}}^p}\;\;\;\;{\rm{for}}\;{\rm{some}}\;\;{\rm{b}}...

Mathematical Notes > 2019 > 105 > 3-4 > 485-502

*L*be a bounded 2 × 2 block operator matrix whose main-diagonal entries are self-adjoint operators. It is assumed that the spectrum of one of these entries is absolutely continuous, being presented by a single finite band, and the spectrum of the other main-diagonal entry is entirely contained in this band. We establish conditions under which the operator matrix

*L*admits a complex deformation and,...

Few-Body Systems > 2017 > 58 > 2 > 1-4

Mathematical Notes > 2016 > 100 > 5-6 > 761-773

*J*-self-adjoint 2 × 2 block operator matrix

*L*in the Feshbach spectral case, that is, in the case where the spectrum of one main-diagonal entry of

*L*is embedded into the absolutely continuous spectrum of the other main-diagonal entry. We work with the analytic continuation of the Schur complement of amain-diagonal entry in

*L*−

*z*to the unphysical sheets of the spectral parameter

*z*plane...

Theoretical and Mathematical Physics > 2016 > 186 > 1 > 83-92

_{0}and σ

_{1}and the set σ

_{1}is in a finite gap of the set σ

_{1}. It is known that if V is a bounded additive self-adjoint perturbation of A that is off-diagonal with respect to the partition spec(A) = σ

_{0}∪ σ

_{1}, then for $$\left\| V \right\| < \sqrt 2 d$$ , where d = dist(σ...

Physics of Atomic Nuclei > 2014 > 77 > 4 > 453-462

*T*matrix and the scattering matrix analytically continued to unphysical energy sheets in a multichannel problem featuring binary channels are discussed. From these representations, it follows that a resonance on a given unphysical sheet arises at the (complex) energy value for which the appropriately truncated scattering matrix considered on the physical sheet has...

Few-Body Systems > 2011 > 51 > 2-4 > 249-257

^{4}He three-atomic system.

Few-Body Systems > 2008 > 44 > 1-4 > 233-236

^{4}He-

^{4}He

_{2}and

^{3}He-

^{4}He

_{2}collisions obtained with the Tang-Toennies-Yiu potential.

Few-Body Systems > 2008 > 43 > 1-4 > 121-127

Few-Body Systems > 2006 > 38 > 2-4 > 115-120

*T*-matrices, scattering matrices, and resolvents continued to the unphysical energy sheets. The description is based on the explicit representations that have been found for analytically continued kernels of the

*T*-operators.

Few-Body Systems > 2006 > 38 > 2-4 > 205-208

^{4}He-

^{4}He

_{2}and

^{3}He-

^{4}He

_{2}collisions. We also study the consequence of varying the coupling constant of the atom-atom interaction.

Integral Equations and Operator Theory > 2005 > 51 > 1 > 121-140

*A*and

*C*be self-adjoint operators such that the spectrum of

*A*lies in a gap of the spectrum of

*C*and let

*d*> 0 be the distance between the spectra of

*A*and

*C*. Under these assumptions we prove that the best possible value of the constant

*c*in the condition $$\left\| B \right\| < cd$$ guaranteeing the existence of a (bounded) solution to the operator Riccati equation

*XA*−

*CX*+

*XBX*=

*B** is...

Few-Body Systems > 2004 > 34 > 1-3 > 137-142

Czechoslovak Journal of Physics > 2002 > 52 > 3 > C649-C654

^{3}He

^{4}He

_{2}three-atomic system. Using these equations we calculate the binding energy of the

^{3}He

^{4}He

_{2}trimer with the LM2M2 potential by Aziz and Slaman and more recent TTY potential by Tang, Toennies and Yiu.