Displaying similar documents to “The link between the kernel method and the method of adjoints for the generalized index 2 F 1 -transform”

The index 2 F 1 -transform of generalized functions

N. Hayek, Benito J. González (1993)

Commentationes Mathematicae Universitatis Carolinae

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In this paper the index transformation F ( τ ) = ∫ 0 ∞ f ( t ) 2 F 1 ( μ + 1 2 + i τ , μ + 1 2 - i τ ; μ + 1 ; - t ) t α d t 2 F 1 ( μ + 1 2 + i τ , μ + 1 2 - i τ ; μ + 1 ; - t ) being the Gauss hypergeometric function, is defined on certain space of generalized functions and its inversion formula established for distributions of compact support on 𝐈 = ( 0 , ∞ ) .

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 ) .

Distributional {D}unkl transform and {D}unkl convolution operators

Jorge J. Betancor (2006)

Bollettino dell'Unione Matematica Italiana

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In this paper, that is divided in two parts, we study the distributional Dunkl transform on R. In the first part we investigate the Dunkl transform and the Dunkl convolution operators on tempered distributions. We prove that the tempered distributions defining Dunkl convolution operators on the Schwartz space ƒ are the elements of 𝒪 c ′ , the space of usual convolution operators on S . In the second part we define the distributional Dunkl transform by employing the kernel method. We introduce...

Indiscernibles and dimensional compactness

C. Ward Henson, Pavol Zlatoš (1996)

Commentationes Mathematicae Universitatis Carolinae

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This is a contribution to the theory of topological vector spaces within the framework of the alternative set theory. Using indiscernibles we will show that every infinite set u S ⊆ G in a biequivalence vector space 〈 W , M , G 〉 , such that x - y ∉ M for distinct x , y ∈ u , contains an infinite independent subset. Consequently, a class X ⊆ G is dimensionally compact iff the π -equivalence ≐ M is compact on X . This solves a problem from the paper [NPZ 1992] by J. Náter, P. Pulmann and the second author.