SECOND-ORDER SUBEXPONENTIAL SEQUENCES AND THE ASYMPTOTIC BEHAVIOR OF THEIR DE PRIL TRANSFORM

Suppose that { f(n), n∈ N 0 } is a sequence of positive real numbers and suppose that the sequence { a(n), n∈ N 0 } is given by a(0) = 0, and, for n≥ 1, by the convolution equation nf(n) = a* f(n). The resulting sequence is denoted by a(n) = ϕ f (n) and is called the De Pril transform of { f(n), n∈ N 0 } . In this paper, we consider first- and second-order asymptotic behavior of { ϕ f (n), n∈ N 0 } for a large class of subexponential sequences { f(n), n∈ N 0 } . We also discuss some applications.