Differential properties of symbols of multidimensional singular integrals in the weighted space of Bessel potentials on the sphere with the weighted functions, having singularities on a sphere are studied. The main results are applied to obtaining theorems on Fourier multipliers of spherical harmonic expansions.

We demonstrate experimentally the generation of an optical beam having an axial focusing that is narrower than the Fourier limit. The beam is constructed from a superposition of Bessel beams with different longitudinal wave vectors, realizing a super-oscillatory axial intensity distribution. Such beams can be useful for microscopy and for optical particle manipulation.

An account on computation of integrals of highly oscillatory functions based on the so-called complex integration methods is presented. Beside the basic idea of this approach some applications in computation of Fourier and Bessel transformations are given. Also, Gaussian quadrature formulas with a modified Hermite weight are considered, including some numerical examples.

Proved are weighted transplantation inequalities for Fourier-Bessel expansions. These extend known results on this subject by considering the largest possible range of parameters, allowing more weights and admitting a shift. The results are then used to produce a fairly general multiplier theorem with power weights for considered expansions. Also fractional integral results and conjugate functi...

Center of pressure (COP) measurements are often used to identify balance problems. A new method for COP signal analysis using mean frequency is proposed in this paper. The computation of mean frequency is based on the Fourier–Bessel (FB) expansion that is suitable for use in non-stationary COP signals. In addition, FB expansion provides better frequency resolution and low frequency detectabilit...

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...

We solve the Cauchy problem for the n-dimensional wave equation, where n is an odd integer, using elementary properties of the Fourier transform. We also show that the solution can be obtained by invoking Bessel functions. The wave equation has a rich history fraught with controversy, both mathematical, see [9], and physical, see [16]. It all started in 1747 when d’Alembert, in a memoir present...

We aim to improve the calculation of near-field head related transfer functions from far-field HRTFs using point source expansions into plane waves. We consider shifted expansions derived using the Fourier-Bessel representation and the Sommerfield-Weyl identity, which are also relevant to field reconstruction with speakers.

In this paper, we will give a certain formula for the Riemann zeta function that expresses the Riemann zeta function by an infinte series consisting of KBessel functions. Such an infinite series expression can be regarded as an analogue of the Chowla-Selberg formula. Roughly speaking, the Chowla-Selberg formula is the formula that expresses the Epstein zeta-function by an infinite series consis...