Extension and lacunas of solutions of linear partial differential equations

DOI10.5802/aif.1520zbMath0853.35022OpenAlexW2326527086MaRDI QIDQ1816863

Uwe Franken, Reinhold Meise

Publication date: 28 November 1996

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1996__46_2_429_0

zbMATH Keywords

Phragmén-Lindelöf conditions for algebraic varietiescontinuous linear right inverses for constants coefficient partial differential operatorsfundamental solutions with lacunasWhitney extension of zero-solutions

Mathematics Subject Classification ID

Topological linear spaces of test functions, distributions and ultradistributions (46F05) Continuation and prolongation of solutions to PDEs (35B60) Plurisubharmonic functions and generalizations (32U05) Fundamental solutions to PDEs and systems of PDEs with constant coefficients (35E05)

Related Items (3)

Local radial Phragmén-Lindelöf estimates for plurisubharmonic functions on analytic varieties ⋮ \(\omega\)-fundamental solutions supported in a half space ⋮ The geometry of analytic varieties satisfying the local Phragmén-Lindelöf condition and a geometric characterization of the partial differential operators that are surjective on $\mathcal \{A\}(\mathbb \{R\}^4)$

Cites Work

• Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse
• Fortsetzungen von \(C^\infty\)-Funktionen, welche auf einer abgeschlossenen Menge in \(R^ n\) definiert sind
• Extension of ultradifferentiable functions
• Continuous linear right inverses for partial differential operators of order 2 and fundamental solutions in half spaces
• Whitney's extension theorem for ultradifferentiable functions of Beurling type
• On the existence of real analytic solutions of partial differential equations with constant coefficients
• On the equivalence of holomorphic and plurisubharmonic Phragmén-Lindelöf principles
• Existence et prolongement des solutions holomorphes des équations aux dérivées partielles. (Existence and prolongation of the holomorphic solutions of partial differential equations)
• Necessary and sufficient conditions for propagation of singularities for systems of linear partial differential operators with constant coefficients
• Linear Extension Operators for Ultradifferentiable Functions of Beurling Type on Compact Sets
• Phragmén-Lindelöf principles on algebraic varieties
• Prolongement des solutions d'une équation aux dérivées partielles à coefficients constants
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