DEPENDENCE OF ASYMPTOTICS OF THE MAJOR EIGENVALUES OF A TRUNCATED CONTINUUM CONVOLUTION ON THE RATE OF SYMBOL MAXIMIZATION

摘要

In this paper, we study the asymptotic behavior of extreme eigenvalues of the operator of the truncated continuum convolution [A_yf](t) = ∫_o~y k(T-s) f(s)da, Y > 0, t ∈ [o,y],with a real-valued symbol K(x) which attains its maximum at one point or at a finite number of points.The main results of the paper arc theorems 2.1 and 2.2, where we prove that the major eigenvalues of the operator Ay tend to M = max K (x) as y -> + ∞ at rate 1/y~v; here v > 0 is the order of zero of the function M - K(x).