Displaying similar documents to “Analytic regularity for the Bergman kernel”

On the analyticity of generalized eigenfunctions (case of real variables)

Eberhard Gerlach (1968)

Annales de l'institut Fourier

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On démontre que, dans les espaces fonctionnels propres de Hilbert (avec un noyau reproduisant), formés de fonctions analytiques de n variables dans un domaine G , pour tout opérateur auto-adjoint, les fonctions propres généralisées sont des fonctions réelles-analytiques dans G .

Failure of analytic hypoellipticity in a class of differential operators

Ovidiu Costin, Rodica D. Costin (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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For the hypoelliptic differential operators P = ∂ x 2 + x k ∂ y - x l ∂ t 2 introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of k and l left open in the analysis, the operators P also fail to be analytic hypoelliptic (except for ( k , l ) = ( 0 , 1 ) ), in accordance with Treves’ conjecture. The proof is constructive, suitable for generalization, and relies on evaluating a family of eigenvalues of a non-self-adjoint operator.

Overstability and resonance

Augustin Fruchard, Reinhard Schäfke (2003)

Annales de l’institut Fourier

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We consider a singularity perturbed nonlinear differential equation ε u ' = f ( x ) u + + ε P ( x , u , ε ) which we suppose real analytic for x near some interval [ a , b ] and small | u | , | ε | . We furthermore suppose that 0 is a turning point, namely that x f ( x ) is positive if x ≠ 0 . We prove that the existence of nicely behaved (as ϵ → 0 ) local (at x = 0 ) or global, real analytic or C ∞ solutions is equivalent to the existence of a formal series solution ∑ u n ( x ) ε n with u n analytic at x = 0 . The main tool of a proof is a new “principle of analytic continuation” for...

Analytic disks with boundaries in a maximal real submanifold of 𝐂 2

Franc Forstneric (1987)

Annales de l'institut Fourier

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Let M be a two dimensional totally real submanifold of class C 2 in C 2 . A continuous map F : Δ ‾ → C 2 of the closed unit disk Δ ‾ ⊂ C into C 2 that is holomorphic on the open disk Δ and maps its boundary b Δ into M is called an analytic disk with boundary in M . Given an initial immersed analytic disk F 0 with boundary in M , we describe the existence and behavior of analytic disks near F 0 with boundaries in small perturbations of M in terms of the homology class of the closed curve F 0 ( b Δ ) in M . We also prove a regularity...

Finitely generated ideals in A ( ω )

John Erik Fornaess, M. Ovrelid (1983)

Annales de l'institut Fourier

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The Gleason problem is solved on real analytic pseudoconvex domains in C 2 . In this case the weakly pseudoconvex points can be a two-dimensional subset of the boundary. To reduce the Gleason problem to a ∂ ‾ question it is shown that the set of Kohn-Nirenberg points is at most one-dimensional. In fact, except for a one-dimensional subset, the weakly pseudoconvex boundary points are R -points as studied by Range and therefore allow local sup-norm estimates for ∂ ‾ .

On the Pythagoras numbers of real analytic set germs

José F. Fernando, Jesús M. Ruiz (2005)

Bulletin de la Société Mathématique de France

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We show that (i) the Pythagoras number of a real analytic set germ is the supremum of the Pythagoras numbers of the curve germs it contains, and (ii) every real analytic curve germ is contained in a real analytic surface germ with the same Pythagoras number (or Pythagoras number 2 if the curve is Pythagorean). This gives new examples and counterexamples concerning sums of squares and positive semidefinite analytic function germs.