The State Space Method

1. Front Matter

   Pages i-ix

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2. Discrete Analogs of Canonical Systems with Pseudo-exponential Potential. Definitions and Formulas for the Spectral Matrix Functions

   • Daniel Alpay, Israel Gohberg

   Pages 1-47

3. Matrix-J-unitary Non-commutative Rational Formal Power Series

   • D. Alpay, D.S. Kalyuzhnyı-Verbovetzkiı

   Pages 49-113

4. State/Signal Linear Time-Invariant Systems Theory, Part I: Discrete Time Systems

   • Damir Z. Arov, Olof J. Staffans

   Pages 115-177

5. Conservative Structured Noncommutative Multidimensional Linear Systems

   • Joseph A. Ball, Gilbert Groenewald, Tanit Malakorn

   Pages 179-223

6. The Bezout Integral Operator: Main Property and Underlying Abstract Scheme

   • I. Gohberg, I. Haimovici, M.A. Kaashoek, L. Lerer

   Pages 225-270

Thisvolumeofthe Operator Theory: Advances and Applications series (OTAA) isthe ?rst volume of a new subseries. This subseries is dedicated to connections between the theory of linear operators and the mathematical theory of linear systems and is named Linear Operators and Linear Systems (LOLS).Asthe- isting subseries Advances in Partial Di?erential Equations (ADPE), the new s- series will continue the traditions of the OTAA series and keep the high quality of the volumes. The editors of the new subseries are: Daniel Alpay (Beer–Sheva, - rael), Joseph Ball (Blacksburg, Virginia, USA) and Andr´ ´ e Ran (Amsterdam, The Netherlands). In the last 25–30 years, Mathematical System Theory developed in an ess- tial way. A large part of this development was connected with the use of the state space method. Let us mention for instance the “theory of H control”. The state ? space method allowed to introduce in system theory the modern tools of matrix and operator theory. On the other hand the state space approach had an imp- tant impact on Algebra, Analysis and Operator Theory. In particular it allowed to solve explicitly some problems from interpolation theory, theory of convolution equations, inverse problems for canonical di?erential equations and their discrete analogs. All these directions are planned to be present in the subseries LOLS. The editors and the publisher are inviting authors to submit their manuscripts for publication in this subseries.

• Bezout operator
• Formal power series
• Linear systems
• Matrix
• Potential
• Special functions
• State space method
• convolution
• operator theory
• matrix theory

• Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

  Daniel Alpay

• School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel

  Israel Gohberg

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