Ukrainian Mathematical Journal

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

The Kontorovich-Lebedev integral transform

  • A. M. Gomilko


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, ∞).


Macdonald Function Finite Segment Abel Means 
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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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