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Documents  47B35 | enregistrements trouvés : 4

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I will give a survey of the operator theory that is currently evolving on Hardy spaces of Dirichlet series. We will consider recent results about multiplicative Hankel operators as introduced and studied by Helson and developments building on the Gordon-Hedenmalm theorem on bounded composition operators on the $H^2$ space of Dirichlet series.

47B35 ; 30B50 ; 30H10

Generalizing results of Rossi and Vergne for the holomorphic discrete series on symmetric domains, on the one hand, and of Chailuek and Hall for Toeplitz operators on the ball, on the other hand, we establish existence of analytic continuation of weighted Bergman spaces, in the weight (Wallach) parameter, as well as of the associated Toeplitz operators (with sufficiently nice symbols), on any smoothly bounded strictly pseudoconvex domain. Still further extension to Sobolev spaces of holomorphic functions is likewise treated. Generalizing results of Rossi and Vergne for the holomorphic discrete series on symmetric domains, on the one hand, and of Chailuek and Hall for Toeplitz operators on the ball, on the other hand, we establish existence of analytic continuation of weighted Bergman spaces, in the weight (Wallach) parameter, as well as of the associated Toeplitz operators (with sufficiently nice symbols), on any smoothly bounded strictly pseudoconvex domain. Still ...

47B35 ; 30H20

Let $f$ and $g$ be functions, not identically zero, in the Fock space $F^2$ of $C^n$. We show that the product $T_fT_\bar{g}$ of Toeplitz operators on $F^2$ is bounded if and only if $f= e^p$ and $g= ce^{-p}$, where $c$ is a nonzero constant and $p$ is a linear polynomial.

47B35 ; 30H20

I will report on the results of my recent work with Dmitri Yafaev (Rennes I). We consider functions $\omega$ on the unit circle with a finite number of logarithmic singularities. We study the approximation of $\omega$ by rational functions in the BMO norm. We find the leading term of the asymptotics of the distance in the BMO norm between $\omega$ and the set of rational functions of degree $n$ as $n$ goes to infinity. Our approach relies on the Adamyan-Arov-Krein theorem and on the study of the asymptotic behaviour of singular values of Hankel operators. In particular, we make use of the localisation principle, which allows us to combine the contributions of several singularities in one asymptotic formula. I will report on the results of my recent work with Dmitri Yafaev (Rennes I). We consider functions $\omega$ on the unit circle with a finite number of logarithmic singularities. We study the approximation of $\omega$ by rational functions in the BMO norm. We find the leading term of the asymptotics of the distance in the BMO norm between $\omega$ and the set of rational functions of degree $n$ as $n$ goes to infinity. Our approach relies on the ...

41A20 ; 47B06 ; 47B35

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