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Documents  47B35 | enregistrements trouvés : 6

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Post-edited  Hankel and composition operators on spaces of Dirichlet series Seip, Kristian (Auteur de la Conférence) | CIRM (Editeur )

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.

Multi angle  Truncated Toeplitz operators Câmara, Cristina (Auteur de la Conférence) | CIRM (Editeur )

Toeplitz matrices and operators constitute one of the most important and widely studied classes of non-self-adjoint operators. In this talk we consider truncated Toeplitz operators, a natural generalisation of finite Toeplitz matrices. They appear in various contexts, such as the study of finite interval convolution equations, signal processing, control theory, diffraction problems, hydrodynamics, elasticity, and they play a fundamental role in the study of complex symmetric operators. We will focus mainly on their invertibility and Fredholmness properties, showing in particular that they are equivalent after extension to block Toeplitz operators, and how this can be used to study the spectra of several classes of truncated Toeplitz operators. Toeplitz matrices and operators constitute one of the most important and widely studied classes of non-self-adjoint operators. In this talk we consider truncated Toeplitz operators, a natural generalisation of finite Toeplitz matrices. They appear in various contexts, such as the study of finite interval convolution equations, signal processing, control theory, diffraction problems, hydrodynamics, elasticity, and they play a fundamental role in ...

47B35

Multi angle  The invariant subspace problem: a concrete operator theory approach Gallardo-Gutiérrez, Eva (Auteur de la Conférence) | CIRM (Editeur )

The Invariant Subspace Problem for (separable) Hilbert spaces is a long-standing open question that traces back to Jonhn Von Neumann's works in the fifties asking, in particular, if every bounded linear operator acting on an infinite dimensional separable Hilbert space has a non-trivial closed invariant subspace. Whereas there are well-known classes of bounded linear operators on Hilbert spaces that are known to have non-trivial, closed invariant subspaces (normal operators, compact operators, polynomially compact operators,...), the question of characterizing the lattice of the invariant subspaces of just a particular bounded linear operator is known to be extremely difficult and indeed, it may solve the Invariant Subspace Problem.

In this talk, we will focus on those concrete operators that may solve the Invariant Subspace Problem, presenting some of their main properties, exhibiting old and new examples and recent results about them obtained in collaboration with Prof. Carl Cowen (Indiana University-Purdue University).
The Invariant Subspace Problem for (separable) Hilbert spaces is a long-standing open question that traces back to Jonhn Von Neumann's works in the fifties asking, in particular, if every bounded linear operator acting on an infinite dimensional separable Hilbert space has a non-trivial closed invariant subspace. Whereas there are well-known classes of bounded linear operators on Hilbert spaces that are known to have non-trivial, closed ...

Multi angle  Rational approximation of functions with logarithmic singularities Pushnitski, Alexander (Auteur de la Conférence) | CIRM (Editeur )

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 ...

Multi angle  Products of Toeplitz operators on the Fock space Zhu, Kehe (Auteur de la Conférence) | CIRM (Editeur )

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.

Multi angle  Analytic continuation of Toeplitz operators Englis, Miroslav (Auteur de la Conférence) | CIRM (Editeur )

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 ...

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