Global hypoellipticity for first-order operators on closed smooth manifolds

DOI10.1007/s11854-018-0039-6zbMath1408.35239arXiv1507.08880OpenAlexW3102171721WikidataQ129778871 ScholiaQ129778871MaRDI QIDQ1661518

Todor Gramchev, Fernando de Ávila Silva, Alexandre Kirilov

Publication date: 16 August 2018

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.08880

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Hypoelliptic equations (35H10) PDEs on manifolds (35R01)

Related Items (8)

Partial Fourier series on compact Lie groups ⋮ Global properties of vector fields on compact Lie groups in Komatsu classes. II: Normal forms ⋮ Global hypoellipticity and global solvability for vector fields on compact Lie groups ⋮ Global hypoellipticity for a class of pseudo-differential operators on the torus ⋮ Global analytic hypoellipticity for a class of evolution operators on \(\mathbb{T}^1 \times \mathbb{S}^3\) ⋮ Global hypoellipticity for strongly invariant operators ⋮ Perturbations of globally hypoelliptic operators on closed manifolds ⋮ Time-periodic Gelfand-Shilov spaces and global hypoellipticity on \(\mathbb{T}\times\mathbb{R}^n\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Kernel and symbol criteria for Schatten classes and \(r\)-nuclearity on compact manifolds
• Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticity
• Global solvability and global hypoellipticity for a class of complex vector fields on the 3-torus
• Quantization of pseudo-differential operators on the torus
• Globally hypoelliptic vector fields
• Fourier multipliers, symbols, and nuclearity on compact manifolds
• Schatten classes on compact manifolds: kernel conditions
• Cohomologically rigid vector fields: the Katok conjecture in dimension 3
• Diophantine approximation on planar curves and the distribution of rational points. With an appendix: Sums of two squares near perfect squares by R. C. Vaughan
• Global solutions to involutive systems
• Global hypoellipticity, global solvability and normal form for a class of real vector fields on a torus and application
• Eigenfunction expansions in ℝⁿ
• Global Solvability for a Class of Complex Vector Fields on the Two-Torus
• On the Greenfield-Wallach and Katok conjectures
• Pseudo-Differential Operators and Symmetries
• Globally Hypoelliptic Vector Fields on Compact Surfaces
• Globally Hypoelliptic and Globally Solvable First Order Evolution Equations
• Global Solvability of an Abstract Complex
• Remarks about global analytic hypoellipticity
• Hypoelliptic vector fields and almost periodic motions on the torus Tⁿ
• Quantitative ergodic theorems and their number-theoretic applications
• Remarks on Global Hypoellipticity
• Integro-Differential Operators on Vector Bundles
• Eigenfunction Expansions of Analytic Functions
• On local solvability of linear partial differential equations part I: Necessary conditions
• Global Hypoellipticity and Liouville Numbers

This page was built for publication: Global hypoellipticity for first-order operators on closed smooth manifolds