Integral formulae for special cases of Taylor's functional calculus

D. Albrecht

Displaying similar documents to “Integral formulae for special cases of Taylor's functional calculus”

Vasilescu-Martinelli formula for operators in Banach spaces

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We prove a formula for the Taylor functional calculus for functions analytic in a neighbourhood of the splitting spectrum of an n-tuple of commuting Banach space operators. This generalizes the formula of Vasilescu for Hilbert space operators and is closely related to a recent result of D. W. Albrecht.

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Ernst J. Albrecht, Florian-Horia Vasilescu (1974)

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$H^{\infty}$ functional calculus for an elliptic operator on a half-space with general boundary conditions

Giovanni Dore, Alberto Venni (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $A$ be the $L^{p}$ realization ( $1 < p < \infty$ ) of a differential operator $P (D_{x}, D_{t})$ on $ℝ^{n} \times ℝ^{+}$ with general boundary conditions $B_{k} (D_{x}, D_{t}) u (x, 0) = 0$ ( $1 \leq k \leq m$ ). Here $P$ is a homogeneous polynomial of order $2 m$ in $n + 1$ complex variables that satisfies a suitable ellipticity condition, and for $1 \leq k \leq m$ $B_{k}$ is a homogeneous polynomial of order $m_{k} < 2 m$ ; it is assumed that the usual complementing condition is satisfied. We prove that $A$ is a sectorial operator with a bounded $H^{\infty}$ functional calculus.