The Cayley transform of the generator of a polynomially stable $$C_0$$-semigroup
The Cayley transform of the generator of a polynomially stable $$C_0$$-semigroup
Abstract In this paper, we study the decay rate of the Cayley transform of the generator of a polynomially stable $$C_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> -semigroup. To estimate the decay rate of the Cayley transform, we develop an integral condition on resolvents for polynomial stability. Using this …