Modified Bessel transform on the spaces LǴ<inf>α</inf>

Abstract

We investigate the modified Bessel transform on the spaces ZǴα, α > - 1, by using the Laguerre expansion of their elements. We find the operational formula for this transform and apply it in solving partial differential equations of the form P1 (∂2/∂x2x + α/x) P2 (∂/∂y) u(x,y) = f(x, y) where [0, ∞) ∈y → f(•, y) ∈LǴα is k-times differentiate mapping and P1 and P2 are polynomials with constant coefficients.