Harmonic Analysis, Generalized Wavelets and the Generalized Continuous Wavelet Transform Associated with Laguerre Functions

We consider the family of Laguerre functions φ_λ,m, (λ, m) ∈ ℝ × ℕ, given for all (x,t) ∈ X = [0, + ∞[ × ℝ by φ λ , m ( x , t ) = e iλt e − | λ | x 2 2   L m ( α ) ( | λ | x 2 ) L m ( α ) ( 0 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203753712/177c79e4-b1e6-4968-b8f2-68ff8d714780/content/eq2798.tif"/>