Index transforms associated with products of Whittaker's functions

  • Authors:

  • Semyon B. Yakubovich

  • Affiliations:

  • Department of Pure Mathematics, Faculty of Sciences, University of Porto, Rua de Campo Alegre 687, 4169-007 Porto, Portugal

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2002

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Abstract

Integral transformations with respect to parameters of the products of Whittaker's functions are investigated in the paper. In particular, a class of these transformations involves the Lebedev index transformation with the square of the Macdonald function. Boundedness and inversion properties are derived in the weighted L2-spaces. The methods of Plancherel's theorems and Parseval's equalities for the Fourier, Mellin and Kontorovich-Lebedev transforms are applied.