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Pseudospectral Functions for Canonical Differential Systems

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Modern Analysis and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 191))

Abstract

A pseudospectral function for a canonical differential system is a nondecreasing function on the real line relative to which the eigentransform for the system is a partial isometry. Pseudospectral functions are constructed by means of eigenfunctions and resolvent operators which depend on boundary conditions for the system. Many results hold for Hamiltonians which have selfadjoint matrix values. The most complete results require the definite case, in which it is assumed that the Hamiltonian is nonnegative.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Virginia, P. O. Box 400137, Charlottesville, VA, 22904-4137, USA

    J. Rovnyak

  2. 735 Crawford Avenue, Brooklyn, NY, 11223, USA

    L.A. Sakhnovich

Authors
  1. J. Rovnyak
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  2. L.A. Sakhnovich
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Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Vadim M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    Israel Gohberg

  3. Insitute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivska st., 01601, Kyiv-4, Ukraine

    Anatoly Kochubei , Yurij Berezansky , Myroslav Gorbachuk  & Valentyna Gorbachuk , ,  & 

  4. Department of Mathematical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Gennadiy Popov

  5. Institute of Analysis and Scientific Computing, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Heinz Langer

Additional information

This paper is dedicated to the memory of the great mathematician M. G. Krein.

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Rovnyak, J., Sakhnovich, L. (2009). Pseudospectral Functions for Canonical Differential Systems. In: Adamyan, V.M., et al. Modern Analysis and Applications. Operator Theory: Advances and Applications, vol 191. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9921-4_12

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