Abstract. For any dynamical system, we show that higher variation-norms for the sequence of ergodic bilinear averages of two functions satisfy a large range of bilinear Lp estimates. It follows that, with probability one, the number of fluctuations along this sequence may grow at most polynomially with respect to (the growth of) the underlying scale. These results strengthen previous works of L...

n this article, we prove an lp-lq-version of morgan’s theorem for the generalized bessel transform.

A rigorous analysis of the unstable Bessel resonator with convex output coupler is presented. The Huygens-Fresnel self-consistency equation is solved to extract the first eigenmodes and eigenvalues of the cavity, taking into account the finite apertures of the mirrors. Attention was directed to the dependence of the output transverse profiles; the losses; and the modal-frequency changes on the ...

In this paper, the quaternion Bessel-Fourier moments are introduced. The significance of phase information in quaternion Bessel-Fourier moments is investigated and an accurate estimation method for rotation angle is described. Furthermore, a new set of invariant descriptors based on the magnitude and the phase information of quaternion Bessel-Fourier moments is derived. Experimental results sho...

This survey paper reports on the properties of the fourth-order Bessel-type linear ordinary differential equation, on the generated self-adjoint differential operators in two associated Hilbert function spaces, and on the generalisation of the classical Hankel integral transform. These results are based upon the properties of the classical Bessel and Laguerre second-order differential equations...

We study theoretically and numerically third-harmonic generation (THG) from model geometries (interfaces, slabs, periodic media) illuminated by Bessel beams produced by focusing an annular intensity profile. Bessel beams exhibit a phase and intensity distribution near focus different from Gaussian beams, resulting in distinct THG phase matching properties and coherent scattering directions. Exc...

The Bessel polynomials are the unique polynomial solutions, with constant equal to 1, of the differential equation xy ′′ (x) + (2x+ 2)y ′ (x) − n(n+ 1)y(x) = 0 (1) They are important in certain problems of mathematical physic, for example they arise in the study of electrical networks and when the wave equation is considered on spherical coordinates. Many application may be found in [7]. In rec...

A novel approach of laser-driven acceleration with Bessel beam is presented in this paper. Bessel beam, in contrast to the Gaussian beam, demonstrates “diffractionfree” characteristics in its propagation, which implies potential in laser-driven acceleration. A configuration of Bessel beam truncated by a set of annular slits makes several special regions in its travelling path, where the laser f...

We present a scheme to realize obstruction- and turbulence-tolerant free-space orbital angular momentum (OAM) multiplexing link by using self-healing Bessel beams accompanied by adaptive compensation techniques. Compensation of multiple 16-ary quadrature amplitude modulation (16-QAM) data carrying Bessel beams through emulated atmospheric turbulence and obstructions is demonstrated. The obtaine...