Product approximations for solutions to a class of evolution equations in Hilbert space

Pierre-A. Vuillermot, Walter Wreszinski
2011 Portugaliae Mathematica  
In this article we prove approximation formulae for a class of unitary evolution operators U (t; s) s;t2[0;T ] associated with linear non-autonomous evolution equations of Schrödinger type de...ned in a Hilbert space H. An important feature of the equations we consider is that both the corresponding self-adjoint generators and their domains may depend explicitly on time, whereas the associated quadratic form domains may not. Furthermore the evolution operators we are interested in satisfy the
more » ... uations in a weak sense. Under such conditions the approximation formulae we prove for U (t; s) involve weak operator limits of products of suitable approximating functions taking values in L(H), the algebra of all linear bounded operators on H. Our results may be relevant to the numerical analysis of U (t; s) and we illustrate them by considering two evolution problems in quantum mechanics.
doi:10.4171/pm/1894 fatcat:ayzgtyapbfcbdaecrrcrhbpz5q