this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

For ψ a nontrivial additive character on the finite field Fq, observe that the map t 7→ P x∈Fq ψ(f(x) + tx) is the Fourier transform of the map t 7→ ψ(f(t)). As is well-known, this has a cohomological interpretation, producing a continuous l-adic Galois representation. This paper studies the L-function attached to the k-th symmetric power of this representation using both l-adic and p-adic meth...

the goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--archimedean spacesand also in $p$--banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.

Riesz fractional derivatives of a function, Dα xf(x) (also called Riesz potentials), are defined as fractional powers of the Laplacian. Asymptotic expansions for large x are computed for the Riesz fractional derivatives of the Airy function of the first kind, Ai(x), and the Scorer function, Gi(x). Reduction formulas are provided that allow one to express Riesz potentials of products of Airy fun...

The multivalency approach to generalized Nevanlinna functions established in Wietsma (Indag Math 29:997–1008, 2018) is here extended the related class of Schur giving thereby rise new characterizations for this as well a straightforward function-theoretical proof its factorization. In particular, explains how well-known factorizations two mentioned classes differ from each other. Indeed, by fac...

We systematically characterize the Fabry-Pérot resonator. We derive the generic Airy distribution of a Fabry-Pérot resonator, which equals the internal resonance enhancement factor, and show that all related Airy distributions are obtained by simple scaling factors. We analyze the textbook approaches to the Fabry-Pérot resonator and point out various misconceptions. We verify that the sum of th...

We report accelerating diffusive solutions to the diffusion equation with a constant tensor. The maximum values of density evolve in an fashion described by Airy functions. show behavior for one--dimensional systems, as well general three--dimensional case. also construct modulated modified form solution that retains features.

We study numerically and demonstrate experimentally a novel type of singular optical beams formed by the phase imprinting of an optical vortex into the structure of the three-Airy beams. In contrast to a vortex-free product of three Airy beams, in this type of singular-Airy beam, the vortex in the beam axis causes a twist in the beam transverse intensity profile with propagation. Such a new typ...

some estimates are proved for the generalized fourier-bessel transform in the space (l^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

Surface plasmon polaritons and free-space beams are often coupled through periodic gratings. Here we show that by employing holographic-based techniques for modulating the grating, one can systematically control the amplitude and phase of the free-space beam. Alternatively, arbitrarily shaped surface plasmon can be generated. By using gratings with different periods for the input and output cou...