Boundary-value problems of Hilbert type for linear p-areolar differential equations in the form
N. V. Ralević (1986)
Matematički Vesnik
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N. V. Ralević (1986)
Matematički Vesnik
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Augustin Fruchard, Reinhard Schäfke (2003)
Annales de l’institut Fourier
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We consider a singularity perturbed nonlinear differential equation which we suppose real analytic for near some interval and small , . We furthermore suppose that 0 is a turning point, namely that is positive if . We prove that the existence of nicely behaved (as ) local (at ) or global, real analytic or solutions is equivalent to the existence of a formal series solution with analytic at . The main tool of a proof is a new “principle of analytic continuation” for...
B. Yousefi, S. Foroutan (2005)
Studia Mathematica
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We consider Hilbert spaces of analytic functions on a plane domain Ω and multiplication operators on such spaces induced by functions from . Recently, K. Zhu has given conditions under which the adjoints of multiplication operators on Hilbert spaces of analytic functions belong to the Cowen-Douglas classes. In this paper, we provide some sufficient conditions which give the converse of the main result obtained by K. Zhu. We also characterize the commutant of certain multiplication operators. ...
Pandelis Dodos (2004)
Fundamenta Mathematicae
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Let X be an abelian Polish group. For every analytic Haar-null set A ⊆ X let T(A) be the set of test measures of A. We show that T(A) is always dense and co-analytic in P(X). We prove that if A is compact then T(A) is dense, while if A is non-meager then T(A) is meager. We also strengthen a result of Solecki and we show that for every analytic Haar-null set A, there exists a Borel Haar-null set B ⊇ A such that T(A)∖ T(B) is meager. Finally, under Martin’s Axiom and the negation of...
Gabor Françis, Nicholas Hanges (1998)
Journées équations aux dérivées partielles
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Let be a bounded, convex and open set with real analytic boundary. Let be the tube with base and let be the Bergman kernel of . If is strongly convex, then is analytic away from the boundary diagonal. In the weakly convex case this is no longer true. In this situation, we relate the off diagonal points where analyticity fails to the Trèves curves. These curves are symplectic invariants which are determined by the CR structure of the boundary of . Note that Trèves curves...
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 introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of and left open in the analysis, the operators also fail to be analytic hypoelliptic (except for ), 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.
D. Przeworska-Rolewicz
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Let X be a linear space. Consider a linear equation(*) P(D)x = y, where y ∈ E ⊂ X,with a right invertible operator D ∈ L(X) and, in general, operator coefficients. The main purpose of this paper is to characterize those subspaces E ⊂ X for which all solutions of (*) belong to E (provided that they exist). This leads, even in the classical case of ordinary differential equations with scalar coefficients, to a new class of -functions, which properly contains the classes of analytic functions...
Robert Deville, Vladimir Fonf, Petr Hájek (1996)
Studia Mathematica
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Angus E. Taylor (1937)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Sameer Chavan (2010)
Colloquium Mathematicae
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Let denote a complex, infinite-dimensional, separable Hilbert space, and for any such Hilbert space , let () denote the algebra of bounded linear operators on . We show that for any co-analytic, right-invertible T in (), αT is hypercyclic for every complex α with , where . In particular, every co-analytic, right-invertible T in () is supercyclic.