Weak almost periodic and optimal mild solutions of fractional evolution equations.
Well-posedness of abstract Cauchy problems.
Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions.
Well-posedness of the difference schemes of the high order of accuracy for elliptic equations.
When unit groups of continuous inverse algebras are regular Lie groups
It is a basic fact in infinite-dimensional Lie theory that the unit group of a continuous inverse algebra A is a Lie group. We describe criteria ensuring that the Lie group is regular in Milnor’s sense. Notably, is regular if A is Mackey-complete and locally m-convex.