The H ∞ −calculus and sums of closed operators

By Nigel J. Kalton, Lutz Weis. 2001

355 citations recorded by the source corpus.

Subfields: Astronomy and Astrophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3931214c3d4c989070aa1b1d96a29f5807c48f87

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Citations in the corpus

The Weiss Conjecture for Bounded Analytic Semigroups (2003, methodology): “We will use some ideas from [14] (see in particular the last section of this paper).”
New thoughts on old results of R.T. Seeley (2004, background): “Furthermore, Seeley’s theorem gained new interest in 1987 and 2001, when Dore and Venni [DV87] and lateron Kalton and Weis [ KW01 ] proved that the boundedness of the imaginary powers of AB, the existence of a bounded H ∞ -calculus for AB, respectively, is closely related to the so-called “maximal-r”
Lp-maximal regularity for second order Cauchy problems (2005, methodology): “For the concepts of RH ∞ functional calculus and R-boundedness, we refer to [17], [ 23 ], [36].”
H^\infty functional calculus and square function estimates for Ritt operators (2012, background): “dedness and R-Ritt operators This section starts with some background on R-boundedness, a notion which -by nowplays a prominent role in many questions concerning functional calculi, see in particular [29, 30, 60]. R-boundedness was introduced in [6] and signiﬁcantly developed in [9]. The resulting n”
Erratum to: Perturbation and interpolation theorems for the H∞-calculus with applications to differential operators (2006, methodology): “It was shown in [ 30 ] that an operator with an H ∞ –calculus is R–sectorial if”
Strong solutions for a compressible fluid model of Korteweg type (2008, background): “For proofs and details we refer to [16] and [13].”
Stochastic evolution equations in UMD Banach spaces (2008, background): “space. For each h∈ H we obtain a linear operator Th : E→ γ(H,E) by putting Thx:= h⊗x, x∈ E. Lemma 2.7 ([17]). If Ehas ﬁnite cotype, the family T = Th : khkH ≤ 1 is R-bounded in L(E,γ(H,E)). Following [21], a Banach space E is said to have property (∆) if there exists a constant C∆ such that if (r′ n”
Pseudodifferential operators on Bochner spaces and an application (2006, result): “The result therefore follows from Theorem 3.3 in [ KW01 ].”
Maximal $L^p$-regularity for stochastic evolution equations (2011, background): “oups on Hilbert spaces [59]. (2) Generators of bounded analytic C0-semigroups admitting Gaussian bounds [27]. (3) Generatorsof positive analytic C0-contractionsemigroupson a space Lq(µ), 1 <q<∞ [41]. STOCHASTIC EVOLUTION EQUATIONS 9 (4) Second order uniformly elliptic operators [3, 21] on Lq(R”
Maximal regularity with temporal weights for parabolic problems with inhomogeneous boundary conditions (2012, background): “E) is a bounded operator, and its spectrum is contained in the set (B1/2(1/2))1/2m. This can be seen using the joint functional calculus for ∂t and (−∆n−1)m on Lp,µ R+;Lp(Rn−1;E) , see Theorem 4.5 of [9]. Due to the R-boundedness of the sets (3.4) and (3.5), the operator-valued Fourier-multiplier th”