Abstract. We investigate expansions according to the eigenfunctions of the Dirac differential operator, describing the motion of a particle in quantum mechanics. We get an upper estimate for the square sum of eigenfunctions and show that the expansions have convergence properties similar to those of classical Fourier series.

AMS Subject Classification (1991): 35P10, 81Q05

Received November 1, 1994. (Registered under 5682/2009.)