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A Convolution Operator Related to the Generalized Mehler–Fock and Kontorovich–Lebedev Transforms

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Abstract

In this paper we study a generalization of an index integral involving the product of modified Bessel functions and associated Legendre functions. It is applied to a convolution construction associated with this integral, which is related to the classical Kontorovich–Lebedev and generalized Mehler–Fock transforms. Mapping properties and norm estimates in weighted L p -spaces, 1 ≤ p ≤ 2, are investigated. An application to a class of convolution integral equations is considered. Necessary and sufficient conditions are found for the solvability of these equations in L 2.

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Authors and Affiliations

  1. Department of Mathematics, Center for Research and Development in Mathematics and Applications, University of Aveiro, Campus Universitário de Santiago, 3810-193, Aveiro, Portugal

    M. M. Rodrigues

  2. Department of Mathematics, Center of Mathematics of University of Porto, Faculty of Science, University of Porto, Rua do Campo Alegre No. 687, 4169-007, Porto, Portugal

    N. Vieira

  3. Department of Mathematics, Faculty of Science, University of Porto, Rua do Campo Alegre No. 687, 4169-007, Porto, Portugal

    S. Yakubovich

Authors
  1. M. M. Rodrigues
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  2. N. Vieira
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  3. S. Yakubovich
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Corresponding author

Correspondence to N. Vieira.

Additional information

The work of the N. Vieira and M. M. Rodrigues were supported by Fundação para a Ciência e a Tecnologia via the grants SFRH/BPD/65043/2009, SFRH/BPD/73537/2010, respectively.

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Rodrigues, M.M., Vieira, N. & Yakubovich, S. A Convolution Operator Related to the Generalized Mehler–Fock and Kontorovich–Lebedev Transforms. Results. Math. 63, 511–528 (2013). https://doi.org/10.1007/s00025-011-0214-x

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  • DOI: https://doi.org/10.1007/s00025-011-0214-x

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