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Generalized integral transforms and asymptotics [PDF]

, 2022
Generalized integral transforms, as one of the powerful tools in mathematical physics, has been elaborated in the last fifty years. Their asymptotic analysis through the asymptotic behavior of distributions is also an important research subject, that took attention on different authors. Obviously, it took our attention too.
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Generalization of a Theorem of Boas to a Class of Integral Transforms

Results in Mathematics, 2000
\textit{R. Boas} [Trans. Am. Math. Soc. 40, 287-308 (1936; Zbl 0015.21301)] proved that if \(f\in L^{2}({\mathbb R})\) \(({\mathbb R}=(-\infty,\infty))\), then a necessary and sufficient condition that \(f\) vanishes everywhere on \((-1,1)\) is that \((B(\widetilde{B}f))(\omega)=-\widetilde{f}(\omega)\), where \[ (Bf)(x)={\frac{1}{\pi}}\int^{\infty}_{0}
Tuan, V. Kim, Zayed, Ahmed I.
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Wiener-Hopf Method and Generalized Integral Transforms

Journal of Mathematical Physics, 1969
We consider the class of singular integral equations that can be solved by means of the Wiener-Hopf technique. The resolvent is given as a dispersion relation in the plane of the parameter λ and some physical applications are discussed.
Bassetto, A., Paccanoni, F.
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On Generalized Quaternion Integral Transform and its Applications

Complex Analysis and Operator Theory
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Baliarsingh, Pinakadhar, Sahoo, Swaraj
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A generalized transformed path integral approach for stochastic processes

Journal of Computational Physics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gnana M. Subramaniam, Prakash Vedula
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On a Generalized Bessel Function and an Integral Transform

Mathematische Nachrichten, 1971
Olkha, G. S., Rathie, P. N.
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On (p,q)-Analogues of Laplace-Typed Integral Transforms and Applications

Symmetry, 2021
Jessada Tariboon, Hwajoon Kim, Kamsing Nonlaopon   +2 more
exaly  

A general class of integral transforms and an expression for their convolution formulas

Integral Transforms and Special Functions, 2022
M Rodrigo
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Applications of general integral transform

2023
Abdon Atangana, Ali Akgül
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Generalized convolutions for the Fourier integral transforms and applications

2008
Summary: This paper provides some generalized convolutions for the Fourier integral transforms and treats the applications. Namely, there are six generalized convolutions with weight-function for the Fourier integral transforms. As for applications, the normed ring structures on \(L^1(\mathbb{R}^d)\) are constructed, and the explicit solution in \(L^1(\
Bui Thi Giang, Nguyen Minh Tuan
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