Nonlinear functions and the norm of the propagators of operational equations Academic Article uri icon

abstract

  • We explore the relation between nonlinear functions and the norm functions of the propagators of operational equations in infinite-dimensional spaces. A general criterion is obtained to judge whether a given nonlinear function is the norm function of some C 0-semigroup, the propagator of a wellposed Cauchy problem for an operational equation in an infinite-dimensional space, which gives a solution to an open problem posed in Lin et al. (2010) [6]. Moreover, applying our abstract results, we show the existence of two valuable C 0-semigroups, which one has been seeking. © 2012 Elsevier B.V.

author list (cited authors)

  • Lin, Y. u., Xiao, T., Liang, J., & Huang, T.

citation count

  • 1

publication date

  • December 2012