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On the Eigenvalues of the Lax Operator for the Matrix-valued AKNS System

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Topics in Operator Theory

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 203))

Abstract

We consider the eigenvalues of the matrix AKNS system and establish bounds on the location of eigenvalues and criteria for the nonexistence of eigenvalues. We also identify properties of the system which guarantee that eigenvalues cannot lie on the imaginary axis or can only lie on the imaginary axis. Moreover, we study the deficiency indices of the underlying non-selfadjoint differential operator.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Martin Klaus

Authors
  1. Martin Klaus
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Joseph A. Ball

  2. Department of Mathematics, College of William and Mary, P. O. Box 8795, Williamsburg, VA, 23187-8795, USA

    Vladimir Bolotnikov , Leiba Rodman  & Ilya M. Spitkovsky ,  & 

  3. Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0112

    J. William Helton

Additional information

Dedicated to Israel Gohberg on the occasion of his eightieth birthday

Communicated by J.A. Ball

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© 2010 Birkhäuser Verlag Basel/Switzerland

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Klaus, M. (2010). On the Eigenvalues of the Lax Operator for the Matrix-valued AKNS System. In: Ball, J.A., Bolotnikov, V., Rodman, L., Spitkovsky, I.M., Helton, J.W. (eds) Topics in Operator Theory. Operator Theory: Advances and Applications, vol 203. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0161-0_12

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