Date/Time*/Room: Friday (3/16/2001) at 2:00 pm in 487 Pickard Hall
Department of Mathematics,
University of Texas at Arlington
``Neutral Equations with Causal Operators''
The concept of causal operator (on a function space) is the same as
nonanticipative operator, or abstract Volterra operator.
The equations under consideration are of the form
(Ux)(t) = (Wx)(t),
with t running on some interval I of the real axis, or - in differential setting
(d/dt)(Ux)(t) = (Wx)(t),
under adequate initial (depending on U and the underlying function
space). Generally, the operators involved are causal, but it is pos-
sible to deal with cases when the inverse of such an operator is
of causal type.
We shall present various existence results for the above mentioned
equations, choosing spaces of continuous functions or spaces of
measurable functions as underlying spaces. The results are due to
us, or they are obtained jointly with Dr.Mehran Mahdavi (Bowie State
A case to which we give preference is when the operator U has an
inverse causal operator. Fixed point theorems are the main tool, and
compactness or contractness conditions are coming into consideration.