Displaying similar documents to “Commutators associated to a subfactor and its relative commutants”

Universal functions on nonsimply connected domains

Antonios D. Melas (2001)

Annales de l’institut Fourier

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We establish certain properties for the class 𝒰 ( Ω , ζ 0 ) of universal functions in Ω with respect to the center ζ 0 ∈ Ω , for certain types of connected non-simply connected domains Ω . In the case where ℂ / Ω is discrete we prove that this class is G δ -dense in H ( Ω ) , depends on the center ζ 0 and that the analog of Kahane’s conjecture does not hold.

Some results about Beurling algebras with applications to operator theory

Thomas Vils Pedersen (1995)

Studia Mathematica

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We prove that certain maximal ideals in Beurling algebras on the unit disc have approximate identities, and show the existence of functions with certain properties in these maximal ideals. We then use these results to prove that if T is a bounded operator on a Banach space X satisfying ∥ T n ∥ = O ( n β ) as n → ∞ for some β ≥ 0, then ∑ n = 1 ∞ ∥ ( 1 - T ) n x ∥ / ∥ ( 1 - T ) n - 1 x ∥ diverges for every x ∈ X such that ( 1 - T ) [ β ] + 1 x ≠ 0 .

The null space of the ∂ ¯ -Neumann operator

Lars Hörmander (2004)

Annales de l’institut Fourier

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Let Ω be a complex analytic manifold of dimension n with a hermitian metric and C ∞ boundary, and let □ = ∂ ¯ ∂ ¯ * + ∂ ¯ * ∂ ¯ be the self-adjoint ∂ ¯ -Neumann operator on the space L 0 , q 2 ( Ω ) of forms of type ( 0 , q ) . If the Levi form of ∂ Ω has everywhere at least n - q positive or at least q + 1 negative eigenvalues, it is well known that Ker □ has finite dimension and that the range of □ is the orthogonal complement. In this paper it is proved that dim Ker □ = ∞ if the range of □ is closed and the Levi form of...

Geometric study of the beta-integers for a Perron number and mathematical quasicrystals

Jean-Pierre Gazeau, Jean-Louis Verger-Gaugry (2004)

Journal de Théorie des Nombres de Bordeaux

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We investigate in a geometrical way the point sets of   ℝ   obtained by the   β -numeration that are the   β -integers   ℤ β ⊂ ℤ [ β ]   where   β   is a Perron number. We show that there exist two canonical cut-and-project schemes associated with the   β -numeration, allowing to lift up the   β -integers to some points of the lattice   ℤ m   ( m =   degree of   β ) lying about the dominant eigenspace of the companion matrix of   β  . When   β   is in particular a Pisot number, this framework gives another proof of the fact...

On Müntz rational approximation in multivariables

S. Zhou (1995)

Colloquium Mathematicae

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The present paper shows that for any s sequences of real numbers, each with infinitely many distinct elements, λ n j , j=1,...,s, the rational combinations of x 1 λ m 1 1 x 2 λ m 2 2 . . . x s λ m s s are always dense in C I s .

L -functions of automorphic forms and combinatorics: Dyck paths

Laurent Habsieger, Emmanuel Royer (2004)

Annales de l'Institut Fourier

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We give a combinatorial interpretation for the positive moments of the values at the edge of the critical strip of the L -functions of modular forms of G L ( 2 ) and G L ( 3 ) . We deduce some results about the asymptotics of these moments. We extend this interpretation to the moments twisted by the eigenvalues of Hecke operators.