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Isospectrality for quantum toric integrable systems

Laurent Charles, Álvaro Pelayo, San Vũ Ngoc (2013)

Annales scientifiques de l'École Normale Supérieure

We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians. This type of...

Iterated series and the Hellinger-Toeplitz theorem.

Charles Swartz (1992)

Publicacions Matemàtiques

We show that an iterated double series condition due to Antosik implies the uniform convergence of the double series. An application of Antosik's condition is given to the derivation of a vector form of the Hellinger-Toeplitz theorem.

Iterates and the boundary behavior of the Berezin transform

Jonathan Arazy, Miroslav Engliš (2001)

Annales de l’institut Fourier

Let μ be a measure on a domain Ω in ℂ n such that the Bergman space of holomorphic functions in L 2 ( Ω , μ ) possesses a reproducing kernel K ( x , y ) and K ( x , x ) > 0 ∀ x ∈ Ω . The Berezin transform associated to μ is the integral...

Iterates of a class of discrete linear operators via contraction principle

Octavian Agratini, Ioan A. Rus (2003)

Commentationes Mathematicae Universitatis Carolinae

In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.

Iterates of maps which are non-expansive in Hilbert's projective metric

Jeremy Gunawardena, Cormac Walsh (2003)

Kybernetika

The cycle time of an operator on R n gives information about the long term behaviour of its iterates. We generalise this notion to operators on symmetric cones. We show that these cones, endowed with either Hilbert’s projective metric or Thompson’s metric, satisfy Busemann’s definition of a space of non- positive curvature. We then deduce that, on a strictly convex symmetric cone, the cycle time exists for all maps which are non-expansive in both these metrics. We also review an analogue for the Hilbert...

Iterati di operatori differenziali singolari e funzioni ultradifferenziabili. II

Cristiana Bondioli (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa Nota, che è il seguito della Nota I dallo stesso titolo, si dimostra che l'applicazione X t , legata all'operatore di trasmutazione associato all'operatore singolare P , è un isomorfismo algebrico e topologico tra gli spazi G * s ⁢ P e G * s .

Iterati di operatori differenziali singolari e funzioni ultradifferenziabili

Cristiana Bondioli (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa Nota (cui farà seguito una seconda) si definiscono, tramite iterazione di operatori differenziali singolari su ] 0 , + ∞ [ a coefficienti C ∞ , spazi di funzioni ultradifferenziabili di ordine s > 1 . Un teorema di tipo Paley-Wiener qui dimostrato permette di concludere che i suddetti spazi sono algebricamente isomorfi allo spazio delle funzioni di Gevrey, di ordine s, pari su R .

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