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In the context of a theorem of Richter, we establish a similarity between C0-semigroups of analytic 2-isometries {T(t)}t≥0 acting on a Hilbert space H and the multiplication operator semigroup {Mϕt}t≥0… Click to show full abstract
In the context of a theorem of Richter, we establish a similarity between C0-semigroups of analytic 2-isometries {T(t)}t≥0 acting on a Hilbert space H and the multiplication operator semigroup {Mϕt}t≥0 induced by ϕt(s)=exp(−st) for s in the right-half plane C+ acting boundedly on weighted Dirichlet spaces on C+. As a consequence, we derive a connection with the right shift semigroup {St}t≥0 given by Stf(x)={0f(x−t) if 0≤x≤t, if x>t, acting on a weighted Lebesgue space on the half line R+ and address some applications regarding the study of the invariant subspaces\linebreak of C0-semigroups of analytic 2-isometries.
Journal Title: Revista Matematica Iberoamericana
Year Published: 2018
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