Synopses & Reviews
From the reviews: "This monograph combines operator techniques with state space methods to solve factorization, spectral estimation and interpolation problems arising in control and signal processing. ... In general, the book lays out intricate ideas in a relaxed one-step at time style and hence should be accessible for beginners in the subject. In addition, the novel way in which known material is interrelated should make the book informative for experts as well." (Joseph A. Ball, Mathematical Reviews, Issue 2011 a)
Table of Contents
Preface.- I Basic Operator Theory.- 1 The Wold Decomposition.- 2 Toeplitz and Laurent Operators.- 3 Inner and Outer Functions.- 4 Rational Inner and Outer Functions.- 5 The Naimark Representation.- 6 The Rational Case.- II Finite Section Techniques.- 7 The Levinson Algorithm and Factorization.- 8 Isometric Representations and Factorization.- 9 Signal Processing.- III Riccati Methods.- 10 Riccati Equations and Factorization.- 11 Kalman and Wiener Filtering.- IV Interpolation Theory.- 13 Contractive Nevanlinna-Pick Interpolation.- V Appendices.- 14 A Review of State Space.- 15 The Levinson Algorithm.- Index.