Rational generalized Stieltjes functions

Yıl 2022, Cilt: 5 Sayı: 3, 154 - 167, 15.09.2022

Ivan Kovalyov

https://doi.org/10.33205/cma.1116322

Öz

The rational meromorphic functions on $\mathbb{C}\backslash\mathbb{R}$ are studied. We consider the some classes of one, as the generalized Nevanlinna $\mathbf{N}_{\kappa}$ and generalized Stieltjes $\mathbf{N}_{\kappa}^{k}$ classes. By Euclidean algorithm, we can find indices $\kappa$ and $k$, i.e. determine which class the function belongs to $\mathbf{N}_{\kappa}^{k}$.

Anahtar Kelimeler

rational function, generalized Nevanlinna function, generalized Stieltjes function

Kaynakça

• V. Derkach: On indefinite moment problem and resolvent matrices of Hermitian operators in Krein spaces, Math. Nachr., 184 (1997), 135–166.
• V. Derkach, I. Kovalyov: The Schur algorithm for indefinite Stieltjes moment problem, Math. Nachr., (2017). DOI: 10.1002/mana.201600189.
• V. Derkach: Generalized resolvents of a class of Hermitian operators in a Krein space, Dokl. Akad. Nauk SSSR, 317 (4) (1991), 807–812.
• V. Derkach: On Weyl function and generalized resolvents of a Hermitian operator in a Krein space, Integral Equations Operator Theory, 23 (1995), 387–415 .
• V. A. Derkach, M. M. Malamud: Generalized resolvents and the boundary value problems for Hermitian operators with gaps, J. Funct.Anal., 95 (1) (1991) 1–95.
• I. Kovalyov: A truncated indefinite Stieltjes moment problem, J. Math. Sci., 224 (2017), 509–529.
• I. Kovalyov: Regularization of the indefinite Stieltjes moment problem, Linear Algebra Appl., 594 (2020), 1–28.
• M. G. Krein, H. Langer: Über einige Fortsetzungsprobleme, die eng mit der Theorie Hermitscher Operatoren in Raume $\Pi_{\kappa}$ zusammenhängen, I. Einige Fuktionenklassen und ihre Dahrstellungen, Math. Nachr., 77 (1977), 187–236.
• M. G. Krein, H. Langer: Über einige Fortsetzungsprobleme, die eng mit der Theorie Hermitscher Operatoren in Raume $\Pi_{\kappa}$ zusammenhängen, II, J. of Funct. Analysis, 30 (1978), 390–447.
• M. G. Krein, H. Langer: On some extension problem which are closely connected with the theory of Hermitian operators in a space $\Pi_{\kappa}$ III. Indefinite analogues of the Hamburger and Stieltjes moment problems, Part I, Beiträge zur Anal., 14 (1979), 25–40.
• M. G. Krein, H. Langer: On some extension problem which are closely connected with the theory of Hermitian operators in a space $\Pi_{\kappa}$ III. Indefinite analogues of the Hamburger and Stieltjes moment problems, Part II, Beiträge zur Anal., 15 (1981), 27–45.