Relationships among transforms, convolutions, and first variations.

Kim, Jeong Gyoo; Ko, Jung Won; Park, Chull; Skoug, David

Displaying similar documents to “Relationships among transforms, convolutions, and first variations.”

Integral transforms, convolution products, and first variations.

Kim, Bong Jin, Kim, Byoung Soo, Skoug, David (2004)

International Journal of Mathematics and Mathematical Sciences

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Generalized transforms and convolutions.

Huffman, Timothy, Park, Chull, Skoug, David (1997)

International Journal of Mathematics and Mathematical Sciences

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Stieltjes transforms on new generalized functions.

Schmeelk, John (2001)

International Journal of Mathematics and Mathematical Sciences

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On the polyconvolution with the weight function for the Fourier cosine, Fourier sine, and the Kontorovich-Lebedev integral transforms.

Nguyen Xuan Thao (2010)

Mathematical Problems in Engineering

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Fourier-Feynman transforms of unbounded functionals on abstract Wiener space

Byoung Kim, Il Yoo, Dong Cho (2010)

Open Mathematics

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Huffman, Park and Skoug established several results involving Fourier-Feynman transform and convolution for functionals in a Banach algebra S on the classical Wiener space. Chang, Kim and Yoo extended these results to abstract Wiener space for a more generalized Fresnel class $ℱ_{𝒜_{1}, 𝒜_{2}}$ A1,A2 than the Fresnel class $ℱ$ (B)which corresponds to the Banach algebra S. In this paper we study Fourier-Feynman transform, convolution and first variation of unbounded functionals on abstract Wiener space...

Convolution in Colombeau's Spaces of Generalized Functions; Part I: the Space Ga and the A-integral

Marko Nedeljkov, Stevan Pilipović (1992)

Publications de l'Institut Mathématique

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Relationships of convolution products, generalized transforms and the first variation on function space.

Chang, Seung Jun, Choi, Jae Gil (2002)

International Journal of Mathematics and Mathematical Sciences

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Convolution in Colombeau's spaces of generalized functions. II: The convolution in $𝒢_{a}$ .

Nedeljkov, M., Pilipović, S. (1992)

Publications de l'Institut Mathématique. Nouvelle Série

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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 $f (x) \to D \int_{ℝ_{+}^{2}} \frac{1}{u} (e^{- u cosh (x + v)} + e^{- u cosh (x - v)}) h (u) f (v) d u d v,$ 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...

Integral transforms of Fourier cosine and sine generalized convolution type.

Nguyen Xuan Thao, Vu Kim Tuan, Nguyen Thanh Hong (2007)

International Journal of Mathematics and Mathematical Sciences

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A characterization of Fourier transforms

Philippe Jaming (2010)

Colloquium Mathematicae

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The aim of this paper is to show that, in various situations, the only continuous linear (or not) map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups ℤ/nℤ, the integers ℤ, the torus 𝕋 and the real line. We also ask a related question for the twisted convolution.

Convolution in Colombeau's Spaces of Generalized Functions; Part II: the Convolution in Ga

Marko Nedeljkov, Stevan Pilipović (1992)

Publications de l'Institut Mathématique

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A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics

Navdeep Goel, Kulbir Singh (2013)

International Journal of Applied Mathematics and Computer Science

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The Linear Canonical Transform (LCT) is a four parameter class of integral transform which plays an important role in many fields of signal processing. Well-known transforms such as the Fourier Transform (FT), the FRactional Fourier Transform (FRFT), and the FreSnel Transform (FST) can be seen as special cases of the linear canonical transform. Many properties of the LCT are currently known but the extension of FRFTs and FTs still needs more attention. This paper presents a modified...