Index transforms associated with products of Whittaker's functions
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摘要
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.
论文关键词：44A20,44A15,33C15,33C20,Whittaker function,Macdonald function,Meijer G-function,Fourier transform,Mellin transform,Kontorovich–Lebedev transform,Parseval equality
论文评审过程：Received 14 January 2002, Revised 27 April 2002, Available online 24 October 2002.
论文官网地址：https://doi.org/10.1016/S0377-0427(02)00559-9
