C. Deng
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In this dissertation, we aim to apply Fourier multiplier theory as a unifying method to advance the study of semigroup theory and further develop the Fourier multiplier theory itself.
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In this dissertation, we aim to apply Fourier multiplier theory as a unifying method to advance the study of semigroup theory and further develop the Fourier multiplier theory itself.
We obtain polynomial decay rates for C0-semigroups, assuming that the resolvent grows polynomially at infinity in the complex right half-plane. Our results do not require the semigroup to be uniformly bounded, and for unbounded semigroups, we improve upon previous results by, for example, removing a logarithmic loss on non-Hilbertian Banach spaces.
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We obtain polynomial decay rates for C0-semigroups, assuming that the resolvent grows polynomially at infinity in the complex right half-plane. Our results do not require the semigroup to be uniformly bounded, and for unbounded semigroups, we improve upon previous results by, for example, removing a logarithmic loss on non-Hilbertian Banach spaces.
In this paper we give growth estimates for ‖Tn‖ for n→∞ in the case T is a strongly Kreiss bounded operator on a UMD Banach space X. In several special cases we provide explicit growth rates. This includes known cases such as Hilbert and Lp-spaces, but also intermediate UMD spaces such as non-commutative Lp-spaces and variable Lebesgue spaces.
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In this paper we give growth estimates for ‖Tn‖ for n→∞ in the case T is a strongly Kreiss bounded operator on a UMD Banach space X. In several special cases we provide explicit growth rates. This includes known cases such as Hilbert and Lp-spaces, but also intermediate UMD spaces such as non-commutative Lp-spaces and variable Lebesgue spaces.