Operators of Class $C_0$ with Spectra in Multiply Connected Regions PDF Download
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Author: Adele Zucchi
Publisher: American Mathematical Soc.
ISBN: 0821806262
Category : Mathematics
Languages : en
Pages : 66
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Book Description
In the present paper the author studies the analogue of the class [italic capital]C0 within a class of operators having a functional calculus based on the algebra of bounded holomorphic functions in a finitely connected domain with an analytic boundary. The latter class consists of the operators having the closure of the domain as a spectral set and having no normal direct summands with spectra contained in the boundary of the domain. (If the domain is the disk the preceding class reduces to the class of completely nonunitary contractions.) The basic properties known for the case of the disk, including the model theory, are established. The extension, even the mere construction of the functional calculus, is not routine, in part because it is unknown whether the analogue of Sz.-Nagy's dilation theorem is true in the author's multiply connected setting.
Author: Adele Zucchi
Publisher: American Mathematical Soc.
ISBN: 0821806262
Category : Mathematics
Languages : en
Pages : 66
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Book Description
In the present paper the author studies the analogue of the class [italic capital]C0 within a class of operators having a functional calculus based on the algebra of bounded holomorphic functions in a finitely connected domain with an analytic boundary. The latter class consists of the operators having the closure of the domain as a spectral set and having no normal direct summands with spectra contained in the boundary of the domain. (If the domain is the disk the preceding class reduces to the class of completely nonunitary contractions.) The basic properties known for the case of the disk, including the model theory, are established. The extension, even the mere construction of the functional calculus, is not routine, in part because it is unknown whether the analogue of Sz.-Nagy's dilation theorem is true in the author's multiply connected setting.
Author: H. Araki
Publisher: Springer
ISBN: 3540358501
Category : Mathematics
Languages : en
Pages : 199
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Author: Daniel Alpay
Publisher: Birkhäuser
ISBN: 3034882475
Category : Mathematics
Languages : en
Pages : 568
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Book Description
This volume presents the refereed proceedings of the Conference in Operator The ory in Honour of Moshe Livsic 80th Birthday, held June 29 to July 4, 1997, at the Ben-Gurion University of the Negev (Beer-Sheva, Israel) and at the Weizmann In stitute of Science (Rehovot, Israel). The volume contains papers in operator theory and its applications (understood in a very wide sense), many of them reflecting, 1 directly or indirectly, a profound impact of the work of Moshe Livsic. Moshe (Mikhail Samuilovich) Livsic was born on July 4, 1917, in the small town of Pokotilova near Uman, in the province of Kiev in the Ukraine; his family moved to Odessa when he was four years old. In 1933 he enrolled in the Department of Physics and Mathematics at the Odessa State University, where he became a student of M. G. Krein and an active participant in Krein's seminar - one of the centres where the ideas and methods of functional analysis and operator theory were being developed. Besides M. G. Krein, M. S. Livsic was strongly influenced B. Va. Levin, an outstanding specialist in the theory of analytic functions. A by deep understanding of operator theory as well as function theory and a penetrating search of connections between the two, were to become one of the landmarks of M. S. Livsic's work. M. S. Livsic defended his Ph. D.
Author: Robin Hartshorne
Publisher: American Mathematical Soc.
ISBN: 0821806483
Category : Mathematics
Languages : en
Pages : 111
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Content Description #"November 1997, volume 130, number 617 (first of 4 numbers)."#On t.p. "P" is blackboard bold.#Includes bibliographical references.
Author: Kazuyoshi Kiyohara
Publisher: American Mathematical Soc.
ISBN: 0821806408
Category : Mathematics
Languages : en
Pages : 159
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Book Description
Two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and Kahler-Liouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, that these classes contain many new examples of manifolds with integrable geodesic flow.
Author: E. R. Pike
Publisher: Elsevier
ISBN: 0080540732
Category : Science
Languages : en
Pages : 1831
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Book Description
Scattering is the collision of two objects that results in a change of trajectory and energy. For example, in particle physics, such as electrons, photons, or neutrons are "scattered off" of a target specimen, resulting in a different energy and direction. In the field of electromagnetism, scattering is the random diffusion of electromagnetic radiation from air masses is an aid in the long-range sending of radio signals over geographic obstacles such as mountains. This type of scattering, applied to the field of acoustics, is the spreading of sound in many directions due to irregularities in the transmission medium. Volume I of Scattering will be devoted to basic theoretical ideas, approximation methods, numerical techniques and mathematical modeling. Volume II will be concerned with basic experimental techniques, technological practices, and comparisons with relevant theoretical work including seismology, medical applications, meteorological phenomena and astronomy. This reference will be used by researchers and graduate students in physics, applied physics, biophysics, chemical physics, medical physics, acoustics, geosciences, optics, mathematics, and engineering. This is the first encyclopedic-range work on the topic of scattering theory in quantum mechanics, elastodynamics, acoustics, and electromagnetics. It serves as a comprehensive interdisciplinary presentation of scattering and inverse scattering theory and applications in a wide range of scientific fields, with an emphasis, and details, up-to-date developments. Scattering also places an emphasis on the problems that are still in active current research. The first interdisciplinary reference source on scattering to gather all world expertise in this technique Covers the major aspects of scattering in a common language, helping to widening the knowledge of researchers across disciplines The list of editors, associate editors and contributors reads like an international Who's Who in the interdisciplinary field of scattering
Author: Lindsay Childs
Publisher: American Mathematical Soc.
ISBN: 0821810774
Category : Mathematics
Languages : en
Pages : 133
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Book Description
This volume gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.
Author: Yuval Zvi Flicker
Publisher: American Mathematical Soc.
ISBN: 0821809598
Category : Mathematics
Languages : en
Pages : 127
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Book Description
The trace formula is the most powerful tool currently available to establish liftings of automorphic forms, as predicted by Langlands principle of functionality. The geometric part of the trace formula consists of orbital integrals, and the lifting is based on the fundamental lemma. The latter is an identity of the relevant orbital integrals for the unit elements of the Hecke algebras. This volume concerns a proof of the fundamental lemma in the classically most interesting case of Siegel modular forms, namely the symplectic group Sp(2). These orbital integrals are compared with those on GL(4), twisted by the transpose inverse involution. The technique of proof is elementary. Compact elements are decomposed into their absolutely semi-simple and topologically unipotent parts also in the twisted case; a double coset decomposition of the form H\ G/K--where H is a subgroup containing the centralizer--plays a key role.
Author: Alexandru Aleman
Publisher: Springer Science & Business Media
ISBN: 3034600984
Category : Mathematics
Languages : en
Pages : 135
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Book Description
If H is a Hilbert space and T : H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ? M? Of course the famous invariant subspace problem asks whether or not T has any non-trivial invariant subspaces. This monograph is part of a long line of study of the invariant subspaces of the operator T = M (multiplication by the independent variable z, i. e. , M f = zf )on a z z Hilbert space of analytic functions on a bounded domain G in C. The characterization of these M -invariant subspaces is particularly interesting since it entails both the properties z of the functions inside the domain G, their zero sets for example, as well as the behavior of the functions near the boundary of G. The operator M is not only interesting in its z own right but often serves as a model operator for certain classes of linear operators. By this we mean that given an operator T on H with certain properties (certain subnormal operators or two-isometric operators with the right spectral properties, etc. ), there is a Hilbert space of analytic functions on a domain G for which T is unitarity equivalent to M .
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 788
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