Bessel potential space on the Laguerre hypergroup

Multiresolution Analysis and Haar Wavelets on the Laguerre Hypergroup

In the past decade research on the multiresolution analysis has made considerable progress due to its wide applications. For the basic theory of multiresolution we refer readers to the work in 1, 2 . Recently, we find that a lot of authors try to extend the theory of wavelets on the Euclidean space to nilpotent Lie groups see 3–6 . In this paper we will give the definition of acceptable dilatio...

Littlewood-Paley g-Functions and Multipliers for the Laguerre Hypergroup

The Bessel Scale-Space

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...

Asymptotics of basic Bessel functions and q-Laguerre polynomials

We establish a large n complete asymptotic expansion for q-Laguerre polynomials and a complete asymptotic expansion for a q-Bessel function of large argument. These expansions are needed in our study of an exactly solvable random transfer matrix model for disordered electronic systems. We also give a new derivation of an asymptotic formula due to Littlewood (1907).

Estimates for the Generalized Fourier-Bessel Transform in the Space L2

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.