Hypercyclic and mixing composition operators on $${\mathscr {O}}_M({\mathbb {R}})$$
Hypercyclic and mixing composition operators on $${\mathscr {O}}_M({\mathbb {R}})$$
Abstract In this paper we characterize mixing composition operators acting on the space $${\mathscr {O}}_M({\mathbb {R}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>O</mml:mi> <mml:mi>M</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> of slowly increasing smooth functions. Moreover we relate the mixing property of those operators with the solvability of Abelās functional ā¦