Subspaces that are invariant with respect to generalized translations (Q2640843)

The operator \(T^ s\) of generalized shifts is defined by the equation \({\mathcal D}_ tu(t,s)={\mathcal D}_ su(t,s),\) where \(u(t,0)=f(t),\quad u'_ s(t,0)=0,\) \(T^ sf(t)=u(t,s).\) Here the operator \({\mathcal D}_ t\) has the form \(D_ t=\partial^ 2_ t+(2r+1)t^{-1}\partial_ t,\quad r\geq - .\) The description of spaces, which are invariant with respect to \(T^ s\), is given.