TOEPLITZ-OPERATORS ON WEIGHTED LP SPACES AND ASSOCIATED ASYMPTOTICS

Asymptotic information is found in this paper for finite Toeplitz matrices generated by a piecewise continuous function. The eigenvalues for certain finite matrices are shown to lie near the range of the generating function. An asymptotic formula for ∑f(λi) where λi are the eigenvalues is also given. The basic technique of the paper is to get the above type of asymptotic information by studying the ordinary Toeplitz operators on weighted lp spaces. © 1990 Birkhäuser Verlag.