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Nonselfadjoint Operators and Related Topics

Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992

  • Conference proceedings
  • © 1994
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Overview

Editors:
  1. A. Feintuch
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    You can also search for this editor in PubMed   Google Scholar

  2. I. Gohberg
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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Operator Theory: Advances and Applications (OT, volume 73)

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Table of contents (16 papers)

  1. Front Matter

    Pages I-X
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  2. Joint Spectrum and Discriminant Varieties of Commuting Nonselfadjoint Operators

    • M. S. Livšic, A. S. Markus
    Pages 1-29
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  3. On the differential structure of matrix-valued rational inner functions

    • Daniel Alpay, Laurent Baratchart, Andrea Gombani
    Pages 30-66
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  4. Conservative Dynamical Systems and Nonlinear Livsic-Brodskii Nodes

    • Joseph A. Ball
    Pages 67-95
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  5. Orthogonal Polynomials over Hilbert Modules

    • Asher Ben-Artzi, Israel Gohberg
    Pages 96-126
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  6. Relations of Linking and Duality between Symmetric Gauge Functions

    • Rajendra Bhatia, Chandler Davis
    Pages 127-137
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  7. Julia Operators and Coefficient Problems

    • Gene Christner, Kin Y. Li, James Rovnyak
    Pages 138-181
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  8. Shifts, Realizations and Interpolation, Redux

    • Harry Dym
    Pages 182-243
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  9. Arveson’s Distance Formulae and Robust Stabilization for Linear Time-Varying Systems

    • Avraham Feintuch
    Pages 244-255
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  10. Entire Cyclic Cohomology of Banach Algebras

    • Peter Fillmore, Masoud Khalkhali
    Pages 256-263
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  11. The Bounded Real Characteristic Function and Nehari Extensions

    • P. A. Fuhrmann
    Pages 264-315
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  12. On Isometric Isomorphism between the Second Dual to the “Small” Lipschitz Space and the “Big” Lipschitz Space

    • Leonid Hanin
    Pages 316-324
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  13. Rules for Computer Simplification of the Formulas in Operator Model Theory and Linear Systems

    • J. William Helton, John J. Wavrik
    Pages 325-354
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  14. Some Global Properties of Fractional-Linear Transformations

    • Victor Khatskevich
    Pages 355-361
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  15. Boundary Values of Berezin Symbols

    • Eric Nordgren, Peter Rosenthal
    Pages 362-368
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  16. Generalized Hermite Polynomials and the Bose-Like Oscillator Calculus

    • Marvin Rosenblum
    Pages 369-396
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  17. A General Theory of Sufficient Collections of Norms with a Prescribed Semigroup of Contractions

    • Nahum Zobin, Veronica Zobina
    Pages 397-416
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  18. Back Matter

    Pages 417-422
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Keywords

About this book

Our goal is to find Grabner bases for polynomials in four different sets of expressions: 1 x- , (1 - x)-1 (RESOL) X, 1 x- (1 - xy)-1 (EB) X, , y-1, (1-yx)-1 y, (1_y)-1 (1-x)-1 (preNF) (EB) plus and (1 - xy)1/2 (1 - yx )1/2 (NF) (preNF) plus and Most formulas in the theory of the Nagy-Foias operator model [NF] are polynomials in these expressions where x = T and y = T*. Complicated polynomials can often be simplified by applying "replacement rules". For example, the polynomial (1 - xy)-2 - 2xy(1-xy)-2 + xy2 (1 - xy)-2 -1 simplifies to O. This can be seen by three applications of the replacement rule (1-xy) -1 xy -t (1 - xy)-1 -1 which is true because of the definition of (1-xy)-1. A replacement rule consists of a left hand side (LHS) and a right hand side (RHS). The LHS will always be a monomial. The RHS will be a polynomial whose terms are "simpler" (in a sense to be made precise) than the LHS. An expression is reduced by repeatedly replacing any occurrence of a LHS by the corresponding RHS. The monomials will be well-ordered, so the reduction procedure will terminate after finitely many steps. Our aim is to provide a list of substitution rules for the classes of expressions above. These rules, when implemented on a computer, provide an efficient automatic simplification process. We discuss and define the ordering on monomials later.

Bibliographic Information

  • Book Title: Nonselfadjoint Operators and Related Topics

  • Book Subtitle: Workshop on Operator Theory and Its Applications, Beersheva, February 24–28, 1992

  • Editors: A. Feintuch, I. Gohberg

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8522-5

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1994

  • Hardcover ISBN: 978-3-7643-5097-0Published: 26 August 1994

  • Softcover ISBN: 978-3-0348-9663-4Published: 01 November 2012

  • eBook ISBN: 978-3-0348-8522-5Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: X, 422

  • Topics: Analysis

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