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Whittaker transform on distributions

Author

Listed:
  • M. M. Rodrigues

    (University of Aveiro, Campus Universitário de Santiago)

  • N. Vieira

    (University of Aveiro, Campus Universitário de Santiago)

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.

Suggested Citation

  • M. M. Rodrigues & N. Vieira, 2015. "Whittaker transform on distributions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(2), pages 229-237, April.
    • Handle: RePEc:spr:indpam:v:46:y:2015:i:2:d:10.1007_s13226-015-0127-6
    DOI: 10.1007/s13226-015-0127-6
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