Global (and local) analyticity for second order operators constructed from rigid vector fields on products of tori

DOI10.1090/S0002-9947-96-01573-5zbMath0863.58063arXivmath/9411202MaRDI QIDQ4890019

David S. Tartakoff

Publication date: 12 June 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9411202

zbMATH Keywords

partial differential operatorsglobal analytic hypoellipticityproduct of tori

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Relations of PDEs on manifolds with hyperfunctions (58J15) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items (19)

Analytic regularity for an operator with Trèves curves ⋮ (Semi-)global analytic hypoellipticity for a class of “sums of squares” which fail to be locally analytic hypoelliptic ⋮ Global hypoellipticity and global solvability in Gevrey classes on the \(n\)-dimensional torus ⋮ On the global solvability in Gevrey classes on the \(n\)-dimensional torus ⋮ Regularity of a class of subLaplacians on the 3-dimensional torus ⋮ Global hypoellipticity and simultaneous approximability in ultradifferentiable classes ⋮ Propagation of regularity and global hypoellipticity ⋮ Unnamed Item ⋮ Global \(s\)-solvability and global \(s\)-hypoellipticity for certain perturbations of zero order of systems of constant real vector fields ⋮ Global hypoellipticity and simultaneous approximability ⋮ Global analytic and Gevrey hypoellipticity of sublaplacians under Diophantine conditions ⋮ Global analytic and Gevrey solvability of sublaplacians under Diophantine conditions ⋮ On Gevrey regularity of globally \(C^{\infty}\) hypoelliptic operators ⋮ Global regularity in ultradifferentiable classes ⋮ On Gevrey solvability and regularity ⋮ Fourier analysis for Denjoy–Carleman classes on the torus ⋮ Global analytic regularity for sums of squares of vector fields ⋮ Global analytic, Gevrey and C∞ hypoellipticity on the 3-torus ⋮ On 𝐶^{∞} and Gevrey regularity of sublaplacians

Cites Work

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• On degenerate elliptic operators of infinite type
• Analyticite et iteres reduits d'un systeme de champs de vecteurs
• Singular solutions for sums of squares of vector fields
• Certain sums of Squares of Vector Fields Fail to be Analytic Hypoelliptic
• Local analytic hypoellipticity for □ _b on nondegenerate Cauchy—Riemann manifolds
• Global analyticity for□^bon three dimensional pseudoconvex cr manifolds
• Gevrey Hypoellipticity for Maximally Hypoelliptic Fourth Order Partial Differential Operators
• Existence of certain skew room frames with application to weakly 3‐chromatic linear spaces
• Gevrey hypoellipticity for subelliptic boundary value problems

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