Autor: Kuzhel, S. - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Towards theory of C-symmetries
Autorzy:: Kuzhel, S.
Sudilovskaya, V.
Powiązania:: https://bibliotekanauki.pl/articles/255003.pdf
Data publikacji:: 2017
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Krein space
J-self-adjoint operator
J-symmetric operator
Friedrichs extension
C-symmetry
Opis:: The concept of C-symmetry originally appeared in PT-symmetric quantum mechanics is studied within the Krein spaces framework.
Źródło:: Opuscula Mathematica; 2017, 37, 1; 65-80
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On self-adjoint operators in Krein spaces constructed by Clifford algebra Cl2
Autorzy:: Kuzhel, S.
Patsyuck, O.
Powiązania:: https://bibliotekanauki.pl/articles/256050.pdf
Data publikacji:: 2012
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Krein spaces
extension theory of symmetric operators
operators with empty resolvent set
J-self-adjoint operators
Clifford algebra Cl2
Opis:: Let J and R be anti-commuting fundamental symmetries in a Hilbert space ℘. The operators J and R can be interpreted as basis (generating) elements of the complex Clifford algebra Cl2(J,R) := span{I, J;R, iJR}. An arbitrary non-trivial fundamental symmetry from Cl2(J,R) is determined by the formula [formula]. Let S be a symmetric operator that commutes with Cl2(J,R). The purpose of this paper is to study the sets [formula] of self-adjoint extensions of S in Krein spaces generated by fundamental symmetries [formula]. We show that the sets [formula] and [formula] are unitarily equivalent for different [formula] and describe in detail the structure of operators [formula] with empty resolvent set.
Źródło:: Opuscula Mathematica; 2012, 32, 2; 297-316
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: On operators of transition in Krein spaces
Autorzy:: Grod, A.
Kuzhel, S.
Sudilovskaya, V.
Powiązania:: https://bibliotekanauki.pl/articles/255652.pdf
Data publikacji:: 2011
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Krein spaces
indefinite metrics
operator of transition
operator Riccati equation
Opis:: The paper is devoted to investigation of operators of transition and the corresponding decompositions of Krein spaces. The obtained results are applied to the study of relationship between solutions of operator Riccati equations and properties of the associated operator matrix L. In this way, we complete the known result (see Theorem 5.2 in the paper of S. Albeverio, A. Motovilov, A. Skhalikov, Integral Equ. Oper. Theory 64 (2004), 455-486) and show the equivalence between the existence of a strong solution K (//K// < 1) of the Riccati equation and similarity of the J-self-adjoint operator L to a self-adjoint one.
Źródło:: Opuscula Mathematica; 2011, 31, 1; 49-59
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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