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Displaying similar documents to “On the integral transformation associated with the product of gamma-functions.”

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 , ∞ ) .

On the Fourier cosine—Kontorovich-Lebedev generalized convolution transforms

Nguyen Thanh Hong, Trinh Tuan, Nguyen Xuan Thao (2013)

Applications of Mathematics

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We deal with several classes of integral transformations of the form f ( x ) → D ∫ ℝ + 2 1 u ( e - u cosh ( x + v ) + e - u cosh ( x - v ) ) h ( u ) f ( v ) d u d v , where D is an operator. In case D is the identity operator, we obtain several operator properties on L p ( ℝ + ) with weights for a generalized operator related to the Fourier cosine and the Kontorovich-Lebedev integral transforms. For a class of differential operators of infinite order, we prove the unitary property of these transforms on L 2 ( ℝ + ) and define the inversion formula. Further, for an other class of differential operators...