Showing papers by "Stanley Osher published in 1967"

Canonical forms of certain Volterra integral operators and a method of solving the commutator equations which involve them

Abstract: The similarity properties of Vol terra operators on Lp[0, l ] having reasonably smooth kernels seem to depend entirely on the behavior of the kernel as regards zeros and singularities on the diagonal x = y. If TQ is a Vol terra operator on Lp[0y l ] , then a study of its similarity properties seems to reduce to the following procedure involving the complex kernel G(xy y). (1) Classify G(x, x) according to its zeros and singularities on the interval 0^§a;?gl. (2) Show that To is similar to a unique Tp for Tp a canonical kernel of the class of which G(x, y) belongs. See [ l ] , [2], and [4] for G(x, y) of order a>0 i.e.