Multidimensional circuit synthesis and multivariable dilation theory

DOI10.1007/s11045-010-0123-2zbMath1219.47025OpenAlexW2076074367MaRDI QIDQ632161

Joseph A. Ball

Publication date: 15 March 2011

Published in: Multidimensional Systems and Signal Processing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11045-010-0123-2

zbMATH Keywords

sums of squaresunitary dilationimpedance and scattering functionKalman realizationmultidimensional circuitsmultivariate Christoffel-Darboux formulapositive real lossless function of several variablespositive-kernel decomposition

Mathematics Subject Classification ID

Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Dilations, extensions, compressions of linear operators (47A20) Applications of operator theory in systems, signals, circuits, and control theory (47N70) Scattering theory of linear operators (47A40)

Related Items

Stable symmetric polynomials and the Schur-Agler class ⋮ Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions ⋮ Fejér-Riesz factorizations and the structure of bivariate polynomials orthogonal on the bi-circle ⋮ Extension of the Bessmertnyĭ realization theorem for rational functions of several complex variables ⋮ Rational Cayley inner Herglotz-Agler functions: positive-kernel decompositions and transfer-function realizations ⋮ Rational inner functions in the Schur-Agler class of the polydisk ⋮ The convex invertible cone structure of positive real odd rational matrix functions ⋮ Schur-Agler and Herglotz-Agler classes of functions: positive-kernel decompositions and transfer-function realizations ⋮ Kummert's approach to realization on the bidisk

Cites Work

• Rational inner functions in the Schur-Agler class of the polydisk
• Polynomials with no zeros on the bidisk
• Synthesis of two-dimensional lossless m-ports with prescribed scattering matrix
• Generalized Choi maps in three-dimensional matrix algebra
• New techniques and results in multidimensional problems
• Positive semidefinite biquadratic forms
• Unitary colligations, reproducing kernel Hilbert spaces, and Nevanlinna-Pick interpolation in several variables
• On an inequality of von Neumann and an application of the metric theory of tensor products to operators theory. (Appendix by S. Kaijser and N. Th. Varopoulos.)
• Scattering systems with several evolutions and multidimensional input/state/output systems
• Conservative state-space realizations of dissipative system behaviors
• Unitary dilations for commuting contractions
• Positive extension, Fejér-Riesz factorization and autoregressive filters in two variables
• Nevanlinna-Pick interpolation on the bidisk
• Ando's theorem and sums of squares
• A Schwarz lemma on the polydisk
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item