17 citations · 69 across the 11 of their papers we have counts for
12 papers
On Lax-Phillips scattering matrix of the abstract wave equation
M. Gawlik, A. Glówczyk, S. Kuzhel
The dependence of singularities of scattering matrices of the abstract wave equation on the choice of asymptotically equivalent outgoing/incoming subspaces is studied. The obtained…
Phillips symmetric operators and their extensions
S. Kuzhel, L. Nizhnik
Let be a symmetric operator with equal defect numbers and let be a set of unitary operators in a Hilbert space . The operator is called $\mathf…
Quantum solvable models with nonlocal one point interactions
Sergii Kuzhel, Miloslav Znojil
Within the framework of quantum mechanics working with one-dimensional, manifestly non-Hermitian Hamiltonians the traditional class of the exactly solvable models with loca…
Towards theory of C-symmetries
S. Kuzhel, V. Sudilovskaya
The concept of C-symmetry originally appeared in PT-symmetric quantum mechanics is studied within the Krein spaces framework.
Unbounded C-symmetries and their nonuniqueness
Carl M. Bender, Sergii Kuzhel
It is shown that if the C operator for a PT-symmetric Hamiltonian with simple eigenvalues is not unique, then it is unbounded. Apart from the special cases of finite-matrix Hamilto…
Lax-Phillips scattering theory for PT-symmetric ρ-perturbed operators
Petru A. Cojuhari, Sergii Kuzhel
The S-matrices corresponding to PT-symmetric ρ-perturbed operators are defined and calculated by means of an approach based on an operator-theoretical interpretation of the Lax-Phi…
On elements of the Lax-Phillips scattering scheme for PT-symmetric operators
Sergio Albeverio, Sergii Kuzhel
Generalized PT-symmetric operators acting an a Hilbert space are defined and investigated. The case of PT-symmetric extensions of a symmetric operator is investi…
On J-Self-Adjoint Operators with Stable C-Symmetry
Seppo Hassi, Sergii Kuzhel
The paper is devoted to a development of the theory of self-adjoint operators in Krein spaces (J-self-adjoint operators) involving some additional properties arising from the exist…
PT symmetry, Cartan decompositions, Lie triple systems and Krein space related Clifford algebras
Uwe Guenther, Sergii Kuzhel
Gauged PT quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact an…
On Symmetries in the Theory of Finite Rank Singular Perturbations
Seppo Hassi, Sergii Kuzhel
For a nonnegative self-adjoint operator acting on a Hilbert space singular perturbations of the form are studie…
On pseudo-Hermitian operators with generalized -symmetries
S. Kuzhel
The concept of -symmetries for pseudo-Hermitian Hamiltonians is studied in the Krein space framework. A generalization of -symmetries is suggested.
p-Adic Fractional Differentiation Operator with Point Interactions
S. Kuzhel, S. Torba
Finite rank point perturbations of the -adic fractional differentiation operator are studied. The main attention is paid to the description of operator realizations (in $L…