Journal of Mathematical Sciences

, Volume 231, Issue 4, pp 547–557 | Cite as

Generalized Bessel–Struve Operator and Its Properties

  • Yu. S. Linchuk

We define the generalized Bessel–Struve operator in the space of functions analytic in an arbitrary domain. The conditions of equivalence of the generalized Bessel–Struve operator to the operator of second derivative are investigated. We also describe the commutant of the generalized Bessel–Struve operator and establish its hypercyclicity and chaotic nature.


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  1. 1.
    A. V. Bratishchev, “Chaotic nature of transformations of the space of analytic functions commuting with the Dunkl differentiation,” Vestn. Donsk. Gos. Tekh. Univ., 9, No. 2(41), 196–207 (2009).Google Scholar
  2. 2.
    V. E. Kim, “Hypercyclicity and chaotic character of generalized convolution operators generated by Gel’fond–Leont’ev operators,” Mat. Zamet., 85, No. 6, 849–856 (2009); English translation : Math. Notes, 85, No. 6, 807–813 (2009).Google Scholar
  3. 3.
    Ju. F. Korobeĭnik, “Compound operator equations in generalized derivatives and their applications to Appell sequences,” Mat. Sborn., 102 (144), No. 4, 475–498 (1977); English translation : Math. USSR-Sb., 31, No. 4, 425–443 (1977).Google Scholar
  4. 4.
    Yu. S. Linchuk, “On one class of diagonal operators in the spaces of analytic functions and its application,” Dop. Nats. Acad. Nauk Ukr., No. 3, 25–28 (2014).Google Scholar
  5. 5.
    Yu. S. Linchuk, “Generalized Dunkl–Opdam operator and its properties in the space of functions analytic in domains,” Mat. Meth. Fiz.-Mekh. Polya, 57, No. 4, 7–17 (2014); English translation : J. Math. Sci., 220, No. 1, 1–14 (2017).Google Scholar
  6. 6.
    M. Yu. Tsar’kov, “Isomorphisms of some analytic spaces commuting with a certain power of the operator of differentiation,” Teor. Funk. Funk. Anal. Prilozh., Issue 11, 86–92 (1970).Google Scholar
  7. 7.
    R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, Redwood City (1989).zbMATHGoogle Scholar
  8. 8.
    A. Gasmi and M. Sifi, “Analytic mean-periodic functions associated with the Bessel–Struve operator on a disk,” Glob. J. Pure Appl. Math., 1, No. 1, 55–68 (2005).Google Scholar
  9. 9.
    A. Gasmi and M. Sifi, “The Bessel–Struve intertwining operator on ℂ and mean-periodic functions,” Int. J. Math. & Math. Sci., 2004, No. 59, 3171–3185 (2004).
  10. 10.
    G. Godefroy and J. H. Shapiro, “Operators with dense, invariant, cyclic vector manifolds,” J. Funct. Anal., 98, No. 2, 229–269 (1991).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    K.-G. Grosse-Erdmann, “Universal families and hypercyclic operators,” Bull. Amer. Math. Soc., 36, No. 3, 345–381 (1999).MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    L. Kamoun and S. Negzaoui, “Sonine transform associated with the Bessel–Struve kernel,” Math. Sci. Res. J., 17, No. 8, 208–219 (2013).zbMATHGoogle Scholar
  13. 13.
    L. Kamoun and M. Sifi, “Bessel–Struve intertwining operator and generalized Taylor series on the real line,” Integr. Transf. Spec. Funct., 16, No. 1, 39–55 (2005).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    G. R. MacLane, “Sequences of derivatives and normal families,” J. Analyse Math., 2, No. 1, 72–87 (1952).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    F. Soltani, “Fock spaces for the q-Bessel–Struve kernel,” Bull. Math. Anal. Appl., 4, No. 2, 1–16 (2012).MathSciNetzbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Yu. S. Linchuk
    • 1
  1. 1.Fed’kovych Chernivtsi National UniversityChernivtsiUkraine

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