Since radial positive definite functions on R remain positive definite when restricted to the sphere, it is natural to ask for properties of the zonal series expansion of such functions which relate to properties of the Fourier-Bessel transform of the radial function. We show that the decay of the Gegenbauer coefficients is determined by the behavior of the Fourier-Bessel transform at the origi...

This paper introduces a new method for the development of closed-form spatial Green’s functions for electrostatic problems involving layered dielectrics. The new method utilizes a finite-difference approximation of the spectral domain form of the Green’s function to overcome the tedious numerical integration of the Fourier–Bessel inverse transform that is required to generate the Green’s functi...

We derive completeness criteria for sequences of functions of the form f(xλn), where λn is the nth zero of a suitably chosen entire function. Using these criteria, we construct systems of nonorthogonal Fourier-Bessel functions and their q-analogues, as well as other complete sets of q-special functions. The completeness of certain sets of q-Bessel functions is then used to prove that, if a func...

We develop the nth order Fourier-Bessel series expansion of 1-D functions in the interval (0,α). Hence we establish the sampling theorem for a function with α-bandlimited nth order Hankel transform. The latter statement implies that the function is also Fourier transform αbandlimited. The samples’ locations are given by the roots of nth order Bessel functions. In addition, the sampling distance...

(About Jackson q-Bessel functions) Laplace transform allows to resolve differential equations in the neighborhood of an irregular singular point. The purpose of the article is to study how to apply a basic Borel– Laplace transformation to q-difference equations satisfied by the q-Bessel functions of F.H. Jackson. Connection matrices are obtained between solutions at the origin and solutions at ...

In this note our aim is to point out that certain inequalities for modified Bessel functions of the first and second kind, deduced recently by Laforgia and Natalini, are in fact equivalent to the corresponding Turán type inequalities for these functions. Moreover, we present some new Turán type inequalities for the aforementioned functions and we show that their product is decreasing as a funct...

Indefinite inner product spaces of entire functions and functions analytic inside a disk are considered and their completeness studied. Spaces induced by the rotation invariant reproducing kernels in the form of the generalized hypergeometric function are completely characterized. A particular space generated by the modified Bessel function kernel is utilized to derive an analytic continuation ...

an infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. the two-dimensional coupled thermoelastodynamic pdes are specified based on equations of motion and energy equation, which are uncoupled using nowacki potential functions. the laplace integral transform and bessel-fourier series are u...

To describe joint timeand frequency-selective (doublyselective) channels in mobile broadband wireless communications, we propose to use the finite parameter model based on the same Bessel functions for each tap (Bessel model). An expression of channel estimation mean squared error (MSE) based on the finite parameter models in Orthogonal Frequency Division Multiplexing (OFDM) systems is derived....