In this working paper we suggest some lines of investigation regarding oscillatory Fourier transforms with homogeneous phase. A special case is the solution to the time-dependent free Schrr odinger equation. We consider time-global range-weighted L 2 ? R n+1-estimates. The main tools are Parseval's formula for Fourier transforms on R, orthogonality arguments arising from decomposing L 2 (R n) u...

In the three-dimensional open rectangular domain, problem of identification redefinition function for a partial differential equation with Gerasimov–Caputo-type fractional operator, degeneration, and integral form condition is considered in case 0<??1 order. A positive parameter present mixed derivatives. The solution this studied class regular functions. Fourier series method used, countabl...

where Jν(x) is the Bessel function of the first kind of order ν [1], and =z denotes the imaginary part of z. An extensive table of integral transforms involving the Bessel functions in the kernels is collected in [6]. Since the integration in (2) is with respect to the order of the Bessel function, such a pair of integral transforms is called index transform. Details about many other index tran...

New representations for an integral kernel of the transmutation operator and a regular solution perturbed Bessel equation form $-u^{\prime\prime}+\left(\frac{\ell(\ell+1)}{x^{2}}+q(x)\right)u=\omega^{2}u$ are obtained. The is represented as Fourier-Jacobi series. Neumann series functions uniformly convergent with respect to $\omega$. For coefficients convenient numerical computation recurrent i...

Connections between Hankel transforms of different order for L-functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated.

Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...

A study of the wave dynamics around a multiple cylindrical fishing cage system is carried out under assumption linear water theory and small-amplitude response. The Fourier–Bessel series expansion velocity potential derived for regions enclosed open-water systems immediate vicinity. scattering between cages accounted by employing Graf's addition theorem. porous flexible modeled using Darcy's la...