Differential convergence criteria for operator improper integrals and series

Authors

DOI:

https://doi.org/10.37863/umzh.v73i9.6093

Keywords:

differential signs of convergence of improper integrals and series, general integral criterion for convergence of series

Abstract

UDC 517.382+517.52+517.521.2
We obtain differential convergence criteria for operator improper integrals and series.

References

V. Yu. Slyusarchuk, Nekotorye pry`znaky` sxody`mosty` chy`slovyx ryadov, Matematy`ka segodnya '90, vyp. 6, 94 – 105 (1990).

V. Yu. Slyusarchuk, Zagal`ni teoremy` pro zbizhnist` chy`slovy`x ryadiv, Vy`d-vo Rivnen. texn. un-tu, Rivne (2001).

G. M. Fy`xtengol`cz, Kurs dy`fferency`al`nogo y` y`ntegral`nogo y`schy`sleny`ya, t. 2, Nauka, Moskva (1966).

V. Yu. Slyusarchuk, Nova integral`na oznaka zbizhnosti ryadiv, Mat. stud., 41, № 2, 198 – 200 (2014).

V. Yu. Slyusarchuk, Integral`ni oznaky` zbizhnosti ryadiv, Bukov. mat. zhurn., 2, № 2-3, 208 – 213 (2014).

V. A. Zory`ch, Matematy`chesky`j analy`z, ch. II, Nauka, Moskva (1984).

V. Yu. Slyusarchuk, Operatorny`j analog oznaky` Bertrana, Mat. stud., 35, № 2, 181 – 195 (2011).

Yu. L. Daletskiĭ, M. G. Kreĭn, Устойчивость решений дифференциальных уравнений в банаховом пространстве [[Stability of solutions of differential equations in Banach space]], Nonlinear Analysis and its Applications Series. Izdat. ``Nauka'', Moscow, (1970).

V. Lakshmy`kantam, S. Ly`la, A. A. Martynyuk, Ustojchy`vost` dvy`zheny`ya: metod sravneny`ya, Nauk. dumka, Ky`ev (1991).

N. Danford, Dzh. Shvarcz, Ly`nejnye operatory. Obshhaya teory`ya, t. I, Y`zd-vo y`nostr. ly`t., Moskva (1962).

V. Yu. Slyusarchuk, Umovy` zbizhnosti operatornogo ryadu $sum_{n=1, infty_{n^{-A}}}, Nauk. visn. Cherniv. un-tu. Matematy`ka, vy`p. 485, 113 – 117 (2009).

L. V. Kantorovy`ch, G. P. Aky`lov, Funkcy`onal`nyj analy`z, Nauka, Moskva (1977).

V. Yu. Slyusarchuk, Dy`ferenczial`ni rivnyannya v banaxovomu prostori, Vy`d-vo Nacz. un-tu vod. gosp-va ta pry`rodokory`stuvannya, Rivne (2006).

V. Yu. Slyusarchuk, Operatornyj analog pry`znaka d'Alambera, Matematy`ka s`ogodni '09, vy`p. 15, 101 – 115 (2009).

V. Yu. Slyusarchuk, Operatorny`j analog oznaky` Koshi, Mat. stud., 33, № 1, 97 – 100 (2010).

V. Yu. Slyusarchuk, Uzagal`nennya oznak Abelya ta Dirixle, Ukr. mat. zhurn., 72, № 4, 527 – 539 (2020). DOI: https://doi.org/10.37863/umzh.v72i4.1141

Downloads

Published

16.09.2021

Issue

Section

Research articles

How to Cite

Slyusarchuk, V. Yu. “Differential Convergence Criteria for Operator Improper Integrals and Series”. Ukrains’kyi Matematychnyi Zhurnal, vol. 73, no. 9, Sept. 2021, pp. 1245-59, https://doi.org/10.37863/umzh.v73i9.6093.