Advances in Differential Equations

The Miller scheme in semigroup theory

Rainer Nagel and Eugenio Sinestrari

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In this paper we apply a set-up introduced by R. K. Miller to transform a linear, inhomogeneous Cauchy problem for the generator of a semigroup on a Banach space into a homogeneous one for a matrix operator, which is the generator of a semigroup on a suitable product space. By using restriction theorems and extrapolation spaces we obtain new results for the inhomogeneous Cauchy problem for Hille-Yosida operators in Favard spaces.

Article information

Adv. Differential Equations, Volume 9, Number 3-4 (2004), 387-414.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
Secondary: 34G10: Linear equations [See also 47D06, 47D09] 35G10: Initial value problems for linear higher-order equations 47N20: Applications to differential and integral equations


Nagel, Rainer; Sinestrari, Eugenio. The Miller scheme in semigroup theory. Adv. Differential Equations 9 (2004), no. 3-4, 387--414.

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