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Documents  Hartmann, Andreas | enregistrements trouvés : 7

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Research talks;Analysis and its Applications

Bishop’s operator arose in the fifties as possible candidates for being counterexamples to the Invariant Subspace Problem. Several authors addressed the problem of finding invariant subspaces for some of these operators; but still the general problem is open. In this talk, we shall discuss about recent results on the existence of invariant subspaces which are indeed spectral subspaces for Bishop operators, by providing an extension of a Theorem of Atzmon (Joint work with M. Monsalve-Lopez). Bishop’s operator arose in the fifties as possible candidates for being counterexamples to the Invariant Subspace Problem. Several authors addressed the problem of finding invariant subspaces for some of these operators; but still the general problem is open. In this talk, we shall discuss about recent results on the existence of invariant subspaces which are indeed spectral subspaces for Bishop operators, by providing an extension of a Theorem ...

47A15 ; 47B37 ; 47B38

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Research talks;Analysis and its Applications

This talk will discuss how to study singular rational inner functions (RIFs) using their zero set behaviors. In the two-variable setting, zero sets can be used to define a quantity called contact order, which helps quantify derivative integrability and non-tangential regularity. In the three-variable and higher setting, the RIF singular sets (and corresponding zero sets) can be much more complicated. We will discuss what holds in general, what holds for simple three-variable RIFs, and some examples illustrating why some of the nice two-variable behavior is lost in higher dimensions. This is joint work with James Pascoe and Alan Sola. This talk will discuss how to study singular rational inner functions (RIFs) using their zero set behaviors. In the two-variable setting, zero sets can be used to define a quantity called contact order, which helps quantify derivative integrability and non-tangential regularity. In the three-variable and higher setting, the RIF singular sets (and corresponding zero sets) can be much more complicated. We will discuss what holds in general, ...

32A20 ; 14C17 ; 14H20 ; 32A35 ; 32A40

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Research talks;Analysis and its Applications

Given a finite positive measure $\mu$ on the unit circle, we consider the distance $e_{n}\left ( \mu \right )$ from $z^{n}$ to the analytic polynomials of degree less than $n$ in $L^{2}\left ( \mu \right )$. We study the asymptotic behavior of $e_{n}\left ( \mu \right )$ for $n\rightarrow \infty$ when the logarithmic integral of the density of $\mu$ diverges for different classes of measures $\mu$.

42C05

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Research talks;Analysis and its Applications

Let $V$ be an analytic subvariety of a domain $\Omega$ in $\mathbb{C}^{n}$. When does $V$ have the property that every bounded holomorphic function $f$ on $V$ has an extension to a bounded holomorphic function on $\Omega$ with the same norm?
An obvious sufficient condition is if $V$ is a holomorphic retract of $\Omega$. We shall discuss for what domains $\Omega$ this is also necessary.
This is joint work with Łukasz Kosiński.

47-XX ; 46-XX ; 32-XX

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Research talks;Analysis and its Applications

Let $X$ be a Banach space of holomorphic functions on the unit disk. A linear polynomial approximation scheme for $X$ is a sequence of bounded linear operators $T_{n} :X\rightarrow X$ with the property that, for each $f\in X$, the functions $T_{n}\left ( f \right )$ are polynomials converging to $f$ in the norm of the space. We completely characterize those spaces $X$ that admit a linear polynomial approximation scheme. In particular, we show that it is not sufficient merely that polynomials be dense in $X$. (Joint work with Javad Mashreghi). Let $X$ be a Banach space of holomorphic functions on the unit disk. A linear polynomial approximation scheme for $X$ is a sequence of bounded linear operators $T_{n} :X\rightarrow X$ with the property that, for each $f\in X$, the functions $T_{n}\left ( f \right )$ are polynomials converging to $f$ in the norm of the space. We completely characterize those spaces $X$ that admit a linear polynomial approximation scheme. In particular, we show ...

41A10 ; 46B15 ; 46B28

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- 461 p.
ISBN 978-0-8218-1083-5

Mathematical surveys and monographs , 0092

Localisation : Collection 1er étage

théorie des opérateurs # analyse harmonique # classe de Hardy # opérateur de Hankel # fonction holomorphe # opérateur de Toëplitz # interpolation # transformation de Hilbert # approximation polynomiale pondérée # cyclicité # maximal # fonction de Littlewood-Paley # interpolation faible de Marcinkiewicz # filtrage de Wiener # fonction de Riemann # espace de noyau de Hilbert # idéal d'opérateur de Von Neumann # théorie spectrale des opérateurs normaux # inégalité de Von Neumann théorie des opérateurs # analyse harmonique # classe de Hardy # opérateur de Hankel # fonction holomorphe # opérateur de Toëplitz # interpolation # transformation de Hilbert # approximation polynomiale pondérée # cyclicité # maximal # fonction de Littlewood-Paley # interpolation faible de Marcinkiewicz # filtrage de Wiener # fonction de Riemann # espace de noyau de Hilbert # idéal d'opérateur de Von Neumann # théorie spectrale des opérateurs ...

47-02 ; 30-02 ; 93-02 ; 30D55 ; 47B35 ; 47A45 ; 93B05 ; 93C05

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- 439 p.
ISBN 978-0-8218-2876-2

Mathematical surveys and monographs , 0093

Localisation : Collection 1er étage

théorie des opérateurs # analyse harmonique # interpolation libre # théorie des systèmes linéaires # classe Hp # fonction analytique # espace de fonction analytique # espace de fonction linéaire

47-02 ; 30D55 ; 30H05 ; 46Exx ; 47N70

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