Displaying similar documents to “Properties of an abstract pseudoresolvent and well-posedness of the degenerate Cauchy problem”

Empathy theory and the Laplace transform

Niko Sauer (1997)

Banach Center Publications

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This paper is concerned with double families of evolution operators employed in the study of dynamical systems in which cause and effect are represented in different Banach spaces. The main tool is the Laplace transform of vector-valued functions. It is used to define the generator of the double family which is a pair of unbounded linear operators and relates to implicit evolution equations in a direct manner. The characterization of generators for a special class of evolutions is presented. ...

On positive Rockland operators

Pascal Auscher, A. ter Elst, Derek Robinson (1994)

Colloquium Mathematicae

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Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on L p ( G ; d g ) . Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on L 2 we prove that it is closed on each of the L p -spaces, p ∈ 〈 1,∞〉, and that it generates a semigroup S with a smooth kernel K which, with its derivatives, satisfies Gaussian bounds. The semigroup is holomorphic in the open right half-plane on all the L p -spaces, p ∈ [1,∞]....