Displaying similar documents to “The index 2 F 1 -transform of generalized functions”

On K-transform.

Nasim, C. (1981)

International Journal of Mathematics and Mathematical Sciences

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Ridgelet transform on tempered distributions

R. Roopkumar (2010)

Commentationes Mathematicae Universitatis Carolinae

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We prove that ridgelet transform R : 𝒮 ( ℝ 2 ) → 𝒮 ( 𝕐 ) and adjoint ridgelet transform R * : 𝒮 ( 𝕐 ) → 𝒮 ( ℝ 2 ) are continuous, where 𝕐 = ℝ + × ℝ × [ 0 , 2 π ] . We also define the ridgelet transform ℛ on the space 𝒮 ' ( ℝ 2 ) of tempered distributions on ℝ 2 , adjoint ridgelet transform ℛ * on 𝒮 ' ( 𝕐 ) and establish that they are linear, continuous with respect to the weak * -topology, consistent with R , R * respectively, and they satisfy the identity ( ℛ * ∘ ℛ ) ( u ) = u , u ∈ 𝒮 ' ( ℝ 2 ) .