The Kato square root problem on vector bundles with generalised bounded geometry

DOI10.1007/s12220-015-9557-yzbMath1337.58011arXiv1203.0373OpenAlexW3105840362MaRDI QIDQ254280

Lashi Bandara, Alan G. R. McIntosh

Publication date: 8 March 2016

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.0373

zbMATH Keywords

Dirac type operatorsgeneralised bounded geometryholomorphic functional calculiKato square root problemquadratic estimatessquare roots of elliptic operators

Mathematics Subject Classification ID

Functional calculus for linear operators (47A60) General theory of partial differential operators (47F05) Elliptic equations on manifolds, general theory (58J05) Linear accretive operators, dissipative operators, etc. (47B44)

Related Items (9)

Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary ⋮ Rough metrics on manifolds and quadratic estimates ⋮ Density problems on vector bundles and manifolds ⋮ Heat kernels and regularity for rough metrics on smooth manifolds ⋮ Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric ⋮ Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in \(L^p\) ⋮ Functional calculus and harmonic analysis in geometry ⋮ Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics ⋮ Self-adjointness of the Gaffney Laplacian on vector bundles

Cites Work

• Quadratic estimates and functional calculi of perturbed Dirac operators
• The solution of the Kato square root problem for second order elliptic operators on \(\mathbb R^n\).
• Quadratic estimates for perturbed Dirac type operators on doubling measure metric spaces
• Boundedness and applications of singular integrals and square functions: a survey
• The Kato square root problem on submanifolds
• On a quadratic estimate related to the Kato conjecture and boundary value problems
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral
• Square roots of perturbed subelliptic operators on Lie groups
• THE KATO SQUARE ROOT PROBLEM FOR MIXED BOUNDARY VALUE PROBLEMS
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