The volume is a careful selection of peer-reviewed papers in operator theory, structured matrices, and dilations, dedicated to Tiberiu Constantinescu, a prominent mathematician in the field.

The extensive survey of J. W. Helton and M. Putinar on positive polynomials, spectral theorem, and optimization is a pioneering essay that, under the unifying concept of positivity, brings together ideas from algebra, algebraic geometry, complex analysis, control theory, mathematical logic, and operator theory.

The other research papers deal with recent advances in the following areas:

• multivariable operator theory
• interpolation and moment problems
• perturbation theory
• composition operators
• matrix completion problems
• systems theory

A publication of the Theta Foundation. Distributed worldwide, except in Romania, by the AMS.

Readership

Graduate students and research mathematicians interested in analysis.

Table of Contents

• D. Alpay, R. W. Buursema, A. Dijksma, and H. Langer -- The combined moment and interpolation problem for Nevanlinna functions
• D. Z. Arov and O. Staffans -- State/signal linear time-invariant systems theory, Part III: Transmission and impedance representations of discrete time systems
• M. Bakonyi and D. Timotin -- The central completion of a positive block operator matrix
• J. A. Ball, V. Bolotnikov, and Q. Fang -- Schur-class multipliers on the Fock space: de Branges-Rovnyak reproducing kernel spaces and transfer-function realizations
• H. Bercovici and W. S. Li -- Invariant subspaces with extremal structure for operators of class $C_0$
• A. K. Beros and D. Sarason -- Composition operators and change of variable in one real dimension
• P. A. Cojuhari -- On the spectrum of a class of block Jacobi matrices
• M. A. Dritschel and S. McCullough -- Test functions, kernels, realizations and interpolation
• Y. Hachez and H. J. Woerdeman -- The Fischer-Frobenius transformation and outer factorization
• S. Hassi, H. S. V. de Snoo, A. E. Sterk, and H. Winkler -- Finite-dimensional graph perturbations of selfadjoint Sturm-Liouville operators
• J. W. Helton and M. Putinar -- Positive polynomials in scalar and matrix variables, the spectral theorem, and optimization
• G. Popescu -- Von Neumann inequality on noncommutative domains
• J. Rovnyak and L. A. Sakhnovich -- Interpolation problems for matrix integro-differential operators with difference kernels and with a finite number of negative squares
• M. C. Tseng and V. Ramakrishna -- Dilation theoretic parametrizations of positive matrices with applications to quantum information