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For a class of non-selfadjoint $h$ –pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin. Specifically, assuming that the quadratic approximations of the principal symbol of the operator along the double characteristics enjoy a partial ellipticity property along a suitable subspace of the phase space, namely their singular space, we give a precise description of...

Eigenvalues of Hille-Tamarkin operators and geometry of Banach function spaces

Thomas Kühn, Mieczysław Mastyło (2011)

Studia Mathematica

We investigate how the asymptotic eigenvalue behaviour of Hille-Tamarkin operators in Banach function spaces depends on the geometry of the spaces involved. It turns out that the relevant properties are cotype p and p-concavity. We prove some eigenvalue estimates for Hille-Tamarkin operators in general Banach function spaces which extend the classical results in Lebesgue spaces. We specialize our results to Lorentz, Orlicz and Zygmund spaces and give applications to Fourier analysis. We are also...

Eigenvalues of Integral Operators, I.

Albrecht Pietsch (1980)

Mathematische Annalen

Eigenvalues of Integral Operators. II.

Albrecht Pietsch (1983)

Mathematische Annalen

Ein neues Surjektivitätskriterium im Hilbertraum.

Hermann Sohr (1981)

Monatshefte für Mathematik

Ein Satz über gewichtete Verschiebungen.

D. Georgijevic (1979)

Publications de l'Institut Mathématique [Elektronische Ressource]

Ein starkes "Null-Zwei"-Gesetz in Lp.

Rainer Wittmann (1988)

Mathematische Zeitschrift

Eine Bemerkung zur Lösung der Operatorgleichung $P (y) = 0$

Staněk, Svatoslav (1970)

Matematický časopis

Eine Charakterisierung der Boole'schen Algebra zu einer ...-direkten Zerlegung.

Michael Tidten (1975)

Manuscripta mathematica

Eine Eigenwertabschätzung für Integraloperatoren mit stochastischen Kernen

Adolf Rhodius (1977)

Commentationes Mathematicae Universitatis Carolinae

Eine Erweiterung des Satzes von Rakovcik und ihre Anwendung in der Simonenko-Theorie.

Frank-Olme Speck (1977)

Mathematische Annalen

Elementary operators and subhomogeneous $C^{*}$ -algebras. II.

Gogić, Ilja (2011)

Banach Journal of Mathematical Analysis [electronic only]

Elementary operators on Banach algebras and Fourier transform

Miloš Arsenović, Dragoljub Kečkić (2006)

Studia Mathematica

We consider elementary operators $x \mapsto \sum_{j = 1}^{n} a_{j} x b_{j}$ , acting on a unital Banach algebra, where $a_{j}$ and $b_{j}$ are separately commuting families of generalized scalar elements. We give an ascent estimate and a lower bound estimate for such an operator. Additionally, we give a weak variant of the Fuglede-Putnam theorem for an elementary operator with strongly commuting families $a_{j}$ and $b_{j}$ , i.e. $a_{j} = a_{j}^{'} + i a_{j}^{''}$ ( $b_{j} = b_{j}^{'} + i b_{j}^{''}$ ), where all $a_{j}^{'}$ and $a_{j}^{''}$ ( $b_{j}^{'}$ and $b_{j}^{''}$ ) commute. The main tool is an L¹ estimate of the Fourier transform of a certain class of $C_{c p t}^{\infty}$ functions...

Elementary operators on prome C*-algebras. I.

Martin Mathieu (1989)

Mathematische Annalen

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