# The Convolution on Time Scales

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In this article,we will show how we can apply complex inversion formula for the inversion of the L2-transform and also express some applications of the L2-transform for solving of singular integral equation (SIEs) with trigonometric kernel and system of partial fractional differential...

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The task of an approximation of a continuous model according to obtained discrete data in its connection with Laplas transformation and z-conversion has been considered. We found that the connection between ordinary differential equations and difference equations has analogy with inverse agreed...

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In this article, we determine the integral transforms of several two-boundary functionals for a difference of a compound Poisson process and a compound renewal process. Another part of the article is devoted to studying the above-mentioned process reflected at its infimum. We use the results...

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Wedge diffraction is a well-known problem in applied mathematics. The currently favoured semi-analytical scheme is to reduce the original elastodynamic equations supplemented with boundary, radiation and tip conditions first to a system of functional equations and then to a system of algebraic...

- Asymptotic behavior of the hitting time, overshoot and undershoot for some L?vy processes. Bernard Roynette; Pierre Vallois; Agn?s Volpi // ESAIM: Probability & Statistics;Jan2008, Vol. 12 Issue 1, p58
?Let (Xt, t?0) be a L?vy process started at , with L?vy measure ?. We consider the first passage time Txof (Xt, t?0) to level x > 0, and Kx:=XTx-x the overshoot and Lx:=x-XTx-the undershoot. We first prove that the Laplace transform of the random triple (Tx,Kx,Lx) satisfies some kind of integral...

- POISSON SUMMATION FORMULA ASSOCIATED WITH THE FRACTIONAL LAPLACE TRANSFORM. DESHMUKH, PRABHAKAR R.; GUDADHE, ALKA S. // Journal of Science & Arts;2013, Vol. 13 Issue 2, p151
The linear canonical transform is four parameterized integral transform, which is an important tool in signal processing and optics. The application of linear canonical transform in quantum mechanics has focused attention on its complex extension. Fractional Laplace transform is a special case...

- INTEGRAL TRANSFORMS AND AMERICAN OPTIONS: LAPLACE AND MELLIN GO GREEN. ALOBAIDI, G.; MALLIER, R.; HASLAM, M. C. // Acta Mathematica Universitatis Comenianae;2014, Vol. 83 Issue 2, p245
We use Mellin and Laplace transforms to study the price of American options, and show that both transforms produce solutions and integral equations which are equivalent to the Green's function approach. Conventional rather than partial transforms are used. We also combine a boundary fixing...

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We express singular integrals of functions involving solutions of transmission problems via linear combinations of these functions with fractional-rational coefficients.

- Sharp L2 boundedness of the oscillatory hyper-Hilbert transform along curves. Jie Cheng Chen; Da Shan Fan; Xiang Rong Zhu // Acta Mathematica Sinica;Apr2010, Vol. 26 Issue 4, p653
Consider the oscillatory hyper-Hilbert transform along the curve Î“( t) = ( t p1, t p2, ..., t pn), where Î² > Î± â‰¥ 0 and 0 < p1 < p2 < ... < p n. We prove that H n,Î±,Î² is bounded on L2 if and only if Î² â‰¥ ( n + 1) Î±. Our work extends and improves some known results.