Journal of Mathematical Sciences

, Volume 184, Issue 3, pp 316–330 | Cite as

Asymptotics of integrals connected with a generalized cantor ladder

  • A. I. Nazarov
  • N. V. Rastegaev

The Cantor ladder is naturally involved into various families of selfsimilar functions. Within the framework of such families, we study the asymptotic behavior of some integrals with parameter. Bibliography: 5 titles.


Asymptotic Behavior Asymptotic Expansion Recurrent Relation Homogeneous Equation Main Lemma 
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  1. 1.
    I. A. Sheipak, “On the construction and some properties of self-similar functions in the spaces L p[0, 1]” [in Russian], Mat. Zametki 81, No. 6, 924–938 (2007); English transl.: Math. Notes 81, No. 6, 827-839 (2007).MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    J. E. Hutchinson, “Fractals and self similarity”, Indiana Univ. Math. J. 30, No. 5, 713–747 (1981).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    E. A. Gorin and B. N. Kukushkin, “Integrals related to the Cantor function” [in Russian] Algebra Anal. 15, No. 3, 188–220 (2003); English transl.: St. Petersbg. Math. J. 15, No. 3, 449-468 (2004).MathSciNetCrossRefGoogle Scholar
  4. 4.
    R. A. Gordon, “Some integrals involving the Cantor function”, Am. Math. Month. 116, No. 3, 218–227 (2009).zbMATHCrossRefGoogle Scholar
  5. 5.
    H. Batman and A. Erdélyi, Higher Transcendental Functions, Vol. I, McGraw-Hill, New York (1953).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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