Whittaker transform on distributions

M. M. Rodrigues () and N. Vieira ()
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M. M. Rodrigues: University of Aveiro, Campus Universitário de Santiago
N. Vieira: University of Aveiro, Campus Universitário de Santiago

Indian Journal of Pure and Applied Mathematics, 2015, vol. 46, issue 2, 229-237

Abstract: Abstract The aim of this paper is to construct a testing function space equipped with the topology generated by the L v,p -multinorm of the differential operator $${B_x} = - 4{x^2}\frac{{{d^2}}}{{d{x^2}}} - 1 + {x^2} - \mu x, $$ where μ 0, p ∈ [1, ∞[, and its k—iterates B x k where k = 0,1,..., and B x 0 φ = φ. We also introduce the correspondent dual space for the index Whittaker transform on distributions. The existence, uniqueness, imbedding and inversion properties are investigated.

Keywords: Testing-function spaces; distributions; index Whittaker transform; Whittaker functions; special functions (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s13226-015-0127-6

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