Journal of Mathematical Sciences

, Volume 216, Issue 2, pp 263–269 | Cite as

Interpolation Formulas for B-Derivative of the Schlӧmilch J-Polynomial


For Schlömilch polynomials in even and odd Bessel j-functions we prove formulas similar to the Riesz interpolation formula. Bibliography: 8 titles.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge (1995).MATHGoogle Scholar
  2. 2.
    I. A. Kipriyanov and V. V. Katrakhov, “On a class of one-dimensional singular pseudodifferential operators” [in Russian], Mat. Sb. 104 No. 1, 49–68 (1977); English transl.: Math. USSR, Sb. 33, 43–61 (1977).Google Scholar
  3. 3.
    L. N. Lyakhov and E. L. Sanina, “Schlömilch polynomials: Riesz’s interpolation formula for B-derivatives and Bernstein’s inequality for Weyl-Marchaud fractional B-derivatives” Dokl. Akad. Nauk, Ross. Akad. Nauk 417, No. 5, 592–596 (2007); English transl.: Dokl. Math. 76, No. 3, 916–920 (2007).Google Scholar
  4. 4.
    L. N. Lyakhov, “The construction of Dirichlet and de la Vallee-Poussin-Nikol’skii kernels for j-Bessel Fourier integrals” [in Russian], Tr. Mosk. Mat. O.-va 76, No. 1, 67-84 (2015); English transl.: Trans. Mosc. Math. Soc. 2015, 55-69 (2015).Google Scholar
  5. 5.
    B. M. Levitan, “Expansion in Fourier series and integrals with Bessel functions” [in Russian], Usp. Mat. Nauk 6, No. 2, 102-143 (1951).MathSciNetGoogle Scholar
  6. 6.
    B. G. Korenev, Introduction to the Theory of Bessel Functions [in Russian], Nauka, Moscow (1971).MATHGoogle Scholar
  7. 7.
    I. A. Kipriyanov and V. I. Kononenko, “On fundamental solutions of certain singular partial differential equations” [in Russian] Diff. Uravn. 5, No. 8, 1470-1483 (1969); English transl.: Differ. Equations 5, 1082–1091 (1972).Google Scholar
  8. 8.
    S. M. Nikol’skii, Approximation of Functions of Several Variables and Embedding Theorems [in Russian], Nauka, Moscow (1977).Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Voronezh State UniversityVoronezhRussia

Personalised recommendations