Turkish Journal of Mathematics
DOI

Abstract
A convolution semigroup plays an important role İn the theory of probability measure on Lie groups. The basic problem is that one wants to express a semigroup as a LévyKhinckine formula. If (\mu_t)_{t\epsilonR*_+} is a continuous semigroup of probability + measures on a HilbertLie group G, then we define T{\mu_t}f:=\integral f_a\mu_t(da) (f\epsilonC_u(G),t>0 It is apparent that (\mu_t)_t{t\epsilonR*_+} is a contİnuous operator semigroup on the space + C_u ( G) with the İnfinitesimal generator N. The generatİng functional A of this semigroup is defined by A := Iim_t>0 1/t(T_{\mu_t}f(e)  f(e). We have the problem of consliuction of a subspace C{_2) ( G) of C_u ( G) such that the generatİng functional A on C{_(2)} ( G) exists. This result will be used Iater to show that the LevyKhinchine formula holds for HilbertLie groups.
Keywords
Continuous convolution semigroup, operator semigroup, HilbertLie group, Lévy measure, infinitesimal generator, generating functional
First Page
245
Last Page
256
Recommended Citation
COŞKUN, Erdal (1997) "Differentiable Functions and the Generators on A HilbertLie Group," Turkish Journal of Mathematics: Vol. 21: No. 2, Article 13. Available at: https://journals.tubitak.gov.tr/math/vol21/iss2/13