A Fourier generalized convolution transform and applications to integral equations

DOI10.2478/s13540-012-0035-yzbMath1279.44006OpenAlexW2101861517MaRDI QIDQ2849836

Tuan Vu Kim, Nguyen Xuan Thao, Nguyen Thanh Hong

Publication date: 19 September 2013

Published in: Fractional Calculus and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s13540-012-0035-y

zbMATH Keywords

Fourier cosine transformFourier sine transformFourier transformintegral equationHölder inequalityHausdorff-Young inequalityconvolution transformWatson theorem

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Integro-ordinary differential equations (45J05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Inequalities for sums, series and integrals (26D15) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (4)

The explicit solutions for a class of fractional Fourier–Laplace convolution equations ⋮ Wavelet convolution product involving fractional Fourier transform ⋮ Convolution theorem for fractional cosine‐sine transform and its application ⋮ On the Fourier–Laplace convolution transforms

Cites Work

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• On a generalized convolution with a weight-function for Fourier cosine, Fourier and Fourier sine transforms
• Symmetries of integro-differential equations. With applications in mechanics and plasma physics
• Integral transforms of Fourier cosine convolution type
• On a method for the construction of generalized integral convolutions
• Integral transforms related to a generalized convolution
• A class of integral transforms related to the fourier cosine convolution

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