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Izv. Akad. Nauk SSSR Ser. Mat., 1968, Volume 32, Issue 5, Pages 1075–1111 (Mi izv2506)  

This article is cited in 7 scientific papers (total in 8 papers)

A generalized Riemann–Liouville operator and some of its applications

M. M. Dzhrbashyan


Abstract: In this paper we formulate operators which constitute an essential generalization of the Riemann–Liouville fractional integro-differentiation operator. With the aid of these operators fundamentally new analogues of the classical formulas of Cauchy, Schwarz, and Poisson for the representation of analytic and harmonic functions in the interior of a circle are established. These formulas enable us to give a complete structural representation for the broad classes of harmonic and analytic functions associated with the generalized operators. Finally, in this paper we also establish sufficient conditions for the solvability of the Hausdorff and Stieltjes moment problems for some general families of sequences of positive numbers.

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English version:
Mathematics of the USSR-Izvestiya, 1968, 2:5, 1027–1063

Bibliographic databases:

UDC: 517.5
MSC: 47G20, 45E05, 26A42, 47A57
Received: 09.10.1967

Citation: M. M. Dzhrbashyan, “A generalized Riemann–Liouville operator and some of its applications”, Izv. Akad. Nauk SSSR Ser. Mat., 32:5 (1968), 1075–1111; Math. USSR-Izv., 2:5 (1968), 1027–1063

Citation in format AMSBIB
\Bibitem{Dzh68}
\by M.~M.~Dzhrbashyan
\paper A generalized Riemann--Liouville operator and some of its
applications
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1968
\vol 32
\issue 5
\pages 1075--1111
\mathnet{http://mi.mathnet.ru/izv2506}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=233992}
\zmath{https://zbmath.org/?q=an:0174.11701}
\transl
\jour Math. USSR-Izv.
\yr 1968
\vol 2
\issue 5
\pages 1027--1063
\crossref{https://doi.org/10.1070/IM1968v002n05ABEH000699}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. M. Dzhrbashyan, “Theory of factorization of functions meromorphic in the disk”, Math. USSR-Sb., 8:4 (1969), 493–592  mathnet  crossref  mathscinet  zmath
    2. M. M. Dzhrbashyan, V. S. Zakharyan, “Boundary properties of subclasses of meromorphic functions of bounded form”, Math. USSR-Izv., 4:6 (1970), 1273–1354  mathnet  crossref  mathscinet  zmath
    3. M. M. Dzhrbashyan, “The theory of factorization and boundary properties of functins meromorphic in a disc”, Russian Math. Surveys, 28:3 (1973), 1–12  mathnet  crossref  mathscinet  zmath
    4. N. U. Arakelian, A. G. Vitushkin, V. S. Vladimirov, A. A. Gonchar, “Mkhitar Mkrtichevich Dzhrbashyan (on his sixtieth birthday)”, Russian Math. Surveys, 34:2 (1979), 269–275  mathnet  crossref  mathscinet  zmath
    5. A. M. Dzhrbashyan, “Embedding the classes $N\{\omega\}$ of Nevanlinna type”, Izv. Math., 63:4 (1999), 687–705  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. A. G. Butkovskii, S. S. Postnov, E. A. Postnova, “Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation”, Autom. Remote Control, 74:4 (2013), 543–574  mathnet  crossref  mathscinet  zmath  isi
    7. A. M. Jerbashian, “On boundary properties and biorthogonal systems in the spaces A ω 2 ⊂ H 2”, J. Contemp. Mathemat. Anal, 49:1 (2014), 17  crossref
    8. I. I. Bavrin, O. E. Iaremko, “Inverting of generalized Riemann–Liouville operator by means of integral Laplace transform”, Ufa Math. J., 8:3 (2016), 41–48  mathnet  crossref  mathscinet  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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