Displaying similar documents to “The surjectivity of a constant coefficient homogeneous differential operator in the real analytic functions and the geometry of its symbol”

Perturbation results for the local Phragmén-Lindelöf condition and stable homogeneous polynomials.

Rüdiger W. Braun, Reinhold Meise, B. Alan Taylor (2003)

RACSAM

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The local Phragmén-Lindelöf condition for analytic varieties in complex n-space was introduced by Hörmander and plays an important role in various areas of analysis. Recently, new necessary geometric properties for a variety satisfying this condition were derived by the present authors. These results are now applied to investigate the homogeneous polynomials P with real coefficients that are stable in the following sense: Whenever f is a holomorphic function that is defined in some neighborhood...

Extension and lacunas of solutions of linear partial differential equations

Uwe Franken, Reinhold Meise (1996)

Annales de l'institut Fourier

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Let K ⊂ Q be compact, convex sets in ℝ n with K ∘ ≠ ∅ and let P ( D ) be a linear, constant coefficient PDO. It is characterized in various ways when each zero solution of P ( D ) in the space ℰ ( K ) of all C ∞ -functions on K extends to a zero solution in ℰ ( Q ) resp. in ℰ ( ℝ n ) . The most relevant characterizations are in terms of Phragmén-Lindelöf conditions on the zero variety of P in ℂ n and in terms of for P ( D ) with lacunas.

A new characterization of the analytic surfaces in ℂ 3 that satisfy the local Phragmén-Lindelöf condition

Rüdiger W. Braun, Reinhold Meise, B. A. Taylor (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove that an analytic surface V in a neighborhood of the origin in ℂ 3 satisfies the local Phragmén-Lindelöf condition PL loc at the origin if and only if V satisfies the following two conditions: (1) V is nearly hyperbolic; (2) for each real simple curve γ in ℝ 3 and each d ≥ 1 , the (algebraic) limit variety T γ , d V satisfies the strong Phragmén-Lindelöf condition. These conditions are also necessary for any pure k -dimensional analytic variety V to satisify PL loc .

Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse

B. A. Taylor, R. Meise, Dietmar Vogt (1990)

Annales de l'institut Fourier

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Solving a problem of L. Schwartz, those constant coefficient partial differential operators P ( D ) are characterized that admit a continuous linear right inverse on ℰ ( Ω ) or 𝒟 ' ( Ω ) , Ω an open set in R n . For bounded Ω with C 1 -boundary these properties are equivalent to P ( D ) being very hyperbolic. For Ω = R n they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial P .