POINTWISE FOURIER INVERSION - A WAVE-EQUATION APPROACH

Functions of the Laplace operator F(-Delta) can be synthesized from th e solution operator to the wave equation. When F is the characteristic function of [0, R-2], this gives a representation for radial Fourier inversion. A number of topics related to pointwise convergence or dive rgence of such inversion, as R --> infinity, are studied in this artic le. In some cases, including analysis on Euclidean space, spheres, hyp erbolic space, and certain other symmetric spaces, exact formulas for fundamental solutions to wave equations are available. In other cases, parametrices and other tools of microlocal analysis are effective.