This article describes a class of pseudo-differential operators(A??)(x)=F??x?1([max?{|?1(||?||p)|,|?2(||?||p)|}]???ˆ(?)), ??D(Qpn) and ??C; here [max?{|?1(||?||p)|,|?2(||?||p)|}]?? is the symbol operator A?. These operators can be seen as generalization Bessel potentials in p-adic context. We show that family (K?)?>0 convolution kernels attached to generalized A?, ?>0, determine semigroup on Qp...

A very general beam solution of the paraxial wave equation in circular cylindrical coordinates is presented. We call such a field a circular beam (CiB). The complex amplitude of the CiB is described by either the Whittaker functions or the confluent hypergeometric functions and is characterized by three parameters that are complex in the most general situation. The propagation through complex A...

We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit distributions can be expressed as Fredholm determinants of integral operators associated to kernels built out of Meijer G-functions or Wright’s generalized Bessel functions. They generalize in a natural wa...

Ordinary Bessel beams are described in terms of the generalized Lorenz-Mie theory (GLMT) by adopting, for what is to our knowledge the first time in the literature, the integral localized approximation for computing their beam shape coefficients (BSCs) in the expansion of the electromagnetic fields. Numerical results reveal that the beam shape coefficients calculated in this way can adequately ...

Abstract The normalization of the generalized Bessel functions $\mathrm{U}_{\sigma,r}$ U σ , r $(\sigma,r\in \mathbb{C}\mathbbm{)}$ ( ∈ C ) defin...