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On estimates for the Fourier-Bessel integral transform in the space L 2(ℝ+)

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Abstract

Two estimates useful in applications are proved for the Fourier-Bessel integral transform in L 2(ℝ+) as applied to some classes of functions characterized by a generalized modulus of continuity.

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References

  1. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Clarendon, Oxford, 1948; Komkniga, Moscow, 2005).

    Google Scholar 

  2. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (Pergamon Press, Oxford, 1964; Gostekhteorizdat, Moscow, 1972).

    MATH  Google Scholar 

  3. V. S. Vladimirov, Equations of Mathematical Physics (Marcel Dekker, New York, 1971; Nauka, Moscow, 1976).

    Google Scholar 

  4. A. G. Sveshnikov, A. N. Bogolyubov, and V. V. Kravtsov, Lectures on Mathematical Physics (Nauka, Moscow, 2004) [in Russian].

    Google Scholar 

  5. G. N. Watson, Treatise on the Theory of Bessel Functions (Inostrannaya Literatura, Moscow, 1949; Cambridge Univ. Press, Cambridge, 1952).

    Google Scholar 

  6. A. I. Zayed, Handbook of Function and Generalized Function Transformations (CRC, Boca Raton, 1996).

    MATH  Google Scholar 

  7. W. N. Everitt and W. Kalf, “The Bessel Differential Equation and the Hankel Transform,” J. Comput. Appl. Math. 208(1), 3–19 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  8. V. A. Abilov, F. V. Abilova, and M. K. Kerimov, “Some Remarks Concerning the Fourier Transform in the Space L 2(R),” Zh. Vychisl. Mat. Mat. Fiz. 48, 939–945 (2008) [Comput. Math. Math. Phys. 48, 885–891 (2008)].

    MATH  Google Scholar 

  9. I. A. Kipriyanov, Singular Elliptic Boundary Value Problems (Nauka, Fizmatlit, Moscow, 1997) [in Russian].

    MATH  Google Scholar 

  10. B. M. Levitan, “Expansion in Fourier Series and Integrals over Bessel Functions,” Usp. Mat. Nauk 6(2(42)), 102–148 (1951).

    MATH  MathSciNet  Google Scholar 

  11. V. A. Abilov and F. V. Abilova, “Approximation of Functions by Fourier-Bessel Sums,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 3–9 (2001).

  12. S. M. Nikol’skii, Approximation of Functions of Several Variables and Embedding Theorems (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia

    V. A. Abilov

  2. Dagestan State Technical University, pr. Kalinina 70, Makhachkala, 367015, Russia

    F. V. Abilova

  3. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

    M. K. Kerimov

Authors
  1. V. A. Abilov
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  2. F. V. Abilova
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  3. M. K. Kerimov
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Correspondence to V. A. Abilov.

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Original Russian Text © V.A. Abilov, F.V. Abilova, M.K. Kerimov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 7, pp. 1158–1166.

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Abilov, V.A., Abilova, F.V. & Kerimov, M.K. On estimates for the Fourier-Bessel integral transform in the space L 2(ℝ+). Comput. Math. and Math. Phys. 49, 1103–1110 (2009). https://doi.org/10.1134/S0965542509070033

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  • DOI: https://doi.org/10.1134/S0965542509070033

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