If we follow an asexually reproducing population through time, then the amount of time that has passed since the most recent common ancestor (MRCA) of all current individuals lived will change as time progresses. The resulting “MRCA age” process has been studied previously when the population has a constant large size and evolves via the diffusion limit of standard Wright-Fisher dynamics. For a...

A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that the Gaussian provides the umbral image of these functions. We emphasize the role of the spherical Bessel functions and a family of associated auxiliary polynomials, as transition elements between these families of functions. The consequences of this point of view a...

In this paper we prove $$L^p$$ estimates for Stein’s square functions associated with Fourier–Bessel expansions. Furthermore, transference results from series to Hankel transforms. Actually, these are vector-valued multipliers discrete continuous in the Bessel setting. As a consequence, deduce sharpness of range p -boundedness corresponding property Hankel–Stein functions. Finally, that ones ha...

The purpose of the present paper is to derive the necessary and sufficient condition for the generalized Bessel function (struve function) belonging to the classes Ωλ(g;α, β) and Υ ∗ λ(g;α, β).

Bessel beams are a family of diffraction-free beams. They have many unique properties and prospective applications. Much attention has been focused to this subject in optics. Recently, the studies of such beams at mmand submmwavebands have been carried out in our group. The investigation results, including their theories, generation, propagation and potential applications, are presented in this...

In this paper, circular Lorentz–Bessel–Gaussian beams (CLBGBs) are introduced as a novel member of the Lorentz-Gaussian family. The analytical expression propagation these passing through paraxial optical ABCD system is derived. generalized Huygens-Fresnel diffraction integral form Collins’s formula and expansion Lorentz distribution in terms complete orthonormal basis set Hermite-Gauss modes u...

In this paper we propose a novel type of scales-spaces which is emerging from the family of inhomogeneous pseudodifferential equations (I − τ∆) t 2 u = f with τ ≥ 0 and scale parameter t ≥ 0. Since they are connected to the convolution semi-group of Bessel potentials we call the associated operators {R t,τ | 0 ≤ τ, t} either Bessel scale-space (τ = 1), R t for short, or scaled Bessel scale-spac...

This paper introduces the concept of Bessel multipliers. These operators are defined by a fixed multiplication pattern, which is inserted between the analysis and synthesis operators. The proposed concept unifies the approach used for Gabor multipliers for arbitrary analysis/synthesis systems, which form Bessel sequences, like wavelet or irregular Gabor frames. The basic properties of this clas...

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...