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- W3008683706 abstract "Abstract For each analytic map $$psi$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>ψ</mml:mi> </mml:math> on the complex plane $$mathbb {C}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>C</mml:mi> </mml:math> , we study the Ritt’s resolvent growth condition for the composition operator $$C_{psi} :f rightarrow fcirc psi$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>ψ</mml:mi> </mml:msub> <mml:mo>:</mml:mo> <mml:mi>f</mml:mi> <mml:mo>→</mml:mo> <mml:mi>f</mml:mi> <mml:mo>∘</mml:mo> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:math> on the Fock space $${mathcal {F}}_2$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> . We show that $$C_{psi}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>ψ</mml:mi> </mml:msub> </mml:math> satisfies such a condition if and only if it is either compact or reduces to the identity operator. As a consequence, it is shown that the Ritt’s resolvent condition and the unconditional Ritt’s condition for $$C_{psi}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>ψ</mml:mi> </mml:msub> </mml:math> are equivalent." @default.
- W3008683706 created "2020-03-06" @default.
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- W3008683706 date "2020-02-17" @default.
- W3008683706 modified "2023-09-25" @default.
- W3008683706 title "Resolvent growth condition for composition operators on the Fock space" @default.
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- W3008683706 doi "https://doi.org/10.1007/s43034-020-00059-9" @default.
- W3008683706 hasPublicationYear "2020" @default.
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