The Functional Calculus for Sectorial Operators

By M. Haase. 2006

1,103 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2c7beab618cace3040127836b1d7f910cf753ea1

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In Applied Mathematics

1. Dachun Yang
2. J. V. Neerven
3. Tuomas Hytönen
4. P. Auscher
5. Mark Veraar
6. Sibei Yang
7. Lutz Weis
8. V. Vijayakumar

In Mathematical Physics

1. Dachun Yang
2. J. V. Neerven
3. Tuomas Hytönen
4. P. Auscher
5. Mark Veraar
6. Lutz Weis
7. Luong Dang Ky
8. Sibei Yang

Citations in the corpus

• Conical square function estimates in UMD Banach spaces and applications to H∞-functional calculi (2007, methodology): “Abovewe have used the inclusion R( √ A) ⊆ R(A), which is true for all sectorial operators (see [11], Corollary 3.”
• Fine scales of decay of operator semigroups (2013, background): “A much fuller account of the calculus for Bernstein functions may be found in the monograph [64], and for the extended calculus in [36].”
• H^\infty functional calculus and square function estimates for Ritt operators (2012, result): “See Section 6 of [45] and Chapter 3 of [23] for similar results.”
• On fractional powers of generators of fractional resolvent families (2010, methodology): “[14] Let b > 0 and A−b is defined as above.”
• Existence of solutions for nonlinear fractional stochastic differential equations (2013, neutral): “2 ([33]).”
• On continuity of solutions for parabolic control systems and input-to-state stability (2017, methodology): “1] and results due to Le Merdy [25], and independently derived by Franks and Grabowski–Callier (see [12] and the references therein).”
• Traces and embeddings of anisotropic function spaces (2012, neutral): “For detailed expositions we refer to [2, 9, 18, 25, 40].”
• Kato's square root problem in Banach spaces (2007, background): “The detailed construction of this calculus, and much more information, can be found in [15, 21, 30].”
• Stochastic Integration in Banach Spaces - a Survey (2013, neutral): “For detailed treatments of the H∞-calculus we refer to [29, 41, 55].”
• Hölder continuous solutions for fractional differential equations and maximal regularity (2013, background): “This functional calculus may be extended in a natural way in order to define the fractional powers A for every ε > 0, see [25, 35].”
• Approximate Controllability Results for Fractional Semilinear Integro-Differential Inclusions in Hilbert Spaces (2015, background): “For a recent work including several examples and properties, we refer the reader to [24].”
• Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates (2013, background): “8) is absolutely convergent in || · ||L(L2(X)) (see [38, 58]).”
• Boundary Value Problems, Weyl Functions, and Differential Operators (2020, background): “The presentation is influenced by personal communication with McKelvey (see also [572]) and lecture notes by Kaltenbäck [451] and Woracek [775, 776]; see also [365, 556, 662] for more references.”
• Lp-maximal regularity for second order Cauchy problems (2005, background): “defines a functional calculus from H ∞ 0 (� β� ) into L(X) (the space of bounded operators on X) for every β � >β . This functional calculus may be extended in a natural way in order to define the fractional powers A e for every e> 0 (see Haase [ 20 ] or”
• The $H^\infty$ functional calculus based on the $S$-spectrum for quaternionic operators and for $n$-tuples of noncommuting operators (2015, neutral): “For an overview and more problems associated with this functional calculus see the paper [41], the book [27] and the references therein.”
• The square root problem for second-order, divergence form operators with mixed boundary conditions on Lp (2012, background): “The definition and further information can be found in [19] or [31].”