Global hypoellipticity for a class of pseudo-differential operators on the torus

DOI10.1007/s00041-018-09645-xzbMath1418.35088arXiv1612.02033OpenAlexW3104230799WikidataQ129097818 ScholiaQ129097818MaRDI QIDQ2003610

Fernando de Ávila Silva, Cleber de Medeira, Rafael Borro Gonzalez, Alexandre Kirilov

Publication date: 9 July 2019

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.02033

zbMATH Keywords

Fourier serieshomogeneous operatorsLiouville numbersobstruction of number-theoretical nature

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Periodic solutions to PDEs (35B10) Hypoelliptic equations (35H10)

Related Items (8)

Partial Fourier series on compact Lie groups ⋮ Globally hypoelliptic triangularizable systems of periodic pseudo‐differential operators ⋮ Global properties of vector fields on compact Lie groups in Komatsu classes. II: Normal forms ⋮ Existence and regularity of periodic solutions for a class of partial differential operators ⋮ Global hypoellipticity for a class of periodic Cauchy operators ⋮ Global analytic hypoellipticity for a class of evolution operators on \(\mathbb{T}^1 \times \mathbb{S}^3\) ⋮ Global hypoellipticity for a class of overdetermined systems of pseudo-differential operators on the torus ⋮ Time-periodic Gelfand-Shilov spaces and global hypoellipticity on \(\mathbb{T}\times\mathbb{R}^n\)

Cites Work

• Unnamed Item
• Unnamed Item
• Global solvability and global hypoellipticity for a class of complex vector fields on the 3-torus
• Existence and regularity of periodic solutions to certain first-order partial differential equations
• On certain non-hypoelliptic vector fields with finite-codimensional range on the three-torus
• Globally hypoelliptic vector fields
• Globally solvable systems of complex vector fields
• Solvability in the large for a class of vector fields on the torus
• Global solvability and hypoellipticity on the torus for a class of differential operators with variable coefficients
• Closedness of the range for vector fields on the torus
• On global hypoellipticity of degenerate elliptic operators
• Global hypoellipticity for first-order operators on closed smooth manifolds
• Normalization of complex-valued planar vector fields which degenerate along a real curve
• Global hypoellipticity and simultaneous approximability
• Cohomologically rigid vector fields: the Katok conjecture in dimension 3
• Globally hypoelliptic systems of vector fields
• Global solvability for a class of overdetermined systems
• ON A PROBLEM POSED BY MAHLER
• On the global solvability for overdetermined systems
• Global solutions to involutive systems
• Global hypoellipticity, global solvability and normal form for a class of real vector fields on a torus and application
• 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
• Remarks about global analytic hypoellipticity
• PERTURBATIONS OF VECTOR FIELDS ON TORI: RESONANT NORMAL FORMS AND DIOPHANTINE PHENOMENA
• Hypoelliptic vector fields and almost periodic motions on the torus Tⁿ
• On local solvability of linear partial differential equations part I: Necessary conditions
• On local solvability of linear partial differential equations—part II. Sufficient conditions
• Global Hypoellipticity and Liouville Numbers

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