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Rational generalized Stieltjes functions

Yıl 2022, Cilt: 5 Sayı: 3, 154 - 167, 15.09.2022
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 $\mathbf{N}_{\kappa}^{k}$.

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.
Yıl 2022, Cilt: 5 Sayı: 3, 154 - 167, 15.09.2022
https://doi.org/10.33205/cma.1116322

Öz

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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Ivan Kovalyov 0000-0001-8464-3377

Yayımlanma Tarihi 15 Eylül 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 3

Kaynak Göster

APA Kovalyov, I. (2022). Rational generalized Stieltjes functions. Constructive Mathematical Analysis, 5(3), 154-167. https://doi.org/10.33205/cma.1116322
AMA Kovalyov I. Rational generalized Stieltjes functions. CMA. Eylül 2022;5(3):154-167. doi:10.33205/cma.1116322
Chicago Kovalyov, Ivan. “Rational Generalized Stieltjes Functions”. Constructive Mathematical Analysis 5, sy. 3 (Eylül 2022): 154-67. https://doi.org/10.33205/cma.1116322.
EndNote Kovalyov I (01 Eylül 2022) Rational generalized Stieltjes functions. Constructive Mathematical Analysis 5 3 154–167.
IEEE I. Kovalyov, “Rational generalized Stieltjes functions”, CMA, c. 5, sy. 3, ss. 154–167, 2022, doi: 10.33205/cma.1116322.
ISNAD Kovalyov, Ivan. “Rational Generalized Stieltjes Functions”. Constructive Mathematical Analysis 5/3 (Eylül 2022), 154-167. https://doi.org/10.33205/cma.1116322.
JAMA Kovalyov I. Rational generalized Stieltjes functions. CMA. 2022;5:154–167.
MLA Kovalyov, Ivan. “Rational Generalized Stieltjes Functions”. Constructive Mathematical Analysis, c. 5, sy. 3, 2022, ss. 154-67, doi:10.33205/cma.1116322.
Vancouver Kovalyov I. Rational generalized Stieltjes functions. CMA. 2022;5(3):154-67.