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Ukrainian Mathematical Journal

, Volume 43, Issue 10, pp 1259–1263 | Cite as

The Kontorovich-Lebedev integral transform

  • A. M. Gomilko
Article

Abstract

One considers the Kontorovich-Lebedev integral transform
$$g (r) = \frac{2}{{\pi ^2 r}} \int\limits_0^\infty {\tau sh} \pi \tau K_{ij} (r) \left( {\int\limits_0^\infty { g} (\rho ) K_{i\tau } (\rho ) d\rho } \right) d\tau , r > 0$$
, r>0, where\(K_{i_\tau } (\rho )\) is the Macdonald function. It is proved that, under the conditiong (ρ) ∈L1, (0, ∞) ∩Lp (0, ∞),p∈(1, ∞), the Abel means of this integral converge to g(r) in theLp(a, b)-norm for any finite segment [a, b] ⊂(0, ∞).

Keywords

Macdonald Function Finite Segment Abel Means 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • A. M. Gomilko
    • 1
  1. 1.Institute of HydromechanicsAcademy of Sciences of the UkraineKiev

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