Systems of finite rank
نویسندگان
چکیده
منابع مشابه
Maximum Rank and Asymptotic Rank of Finite Dynamical Systems
A finite dynamical system is a system of multivariate functions over a finite alphabet. The main feature of a finite dynamical system is its interaction graph, which indicates which local functions depend on which variables. The rank of a finite dynamical system is the cardinality of its image; the asymptotic rank is the number of its periodic points. In this paper, we determine the maximum ran...
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By a finite-rank (linear functional) system, we mean a system of linear differential, shift and q-shift operators or, any mixture thereof, whose solution space is finite-dimensional. This poster attempts to develop an algorithm for factoring finite-rank systems into “subsystems” whose solution spaces are of lower dimension. This work consists of three parts: 1. using module-theoretic language t...
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We use Rokhlin’s Theorem on the uniqueness of canonical systems to find a new way to establish connections between Function Theory in the unit disk and rank one perturbations of self-adjoint or unitary operators. In the n-dimensional case, we prove that for any cyclic self-adjoint operator A, operator Aλ = A + Σ k=1 λk(·, φk)φk is pure point for a.e. λ = (λ1, λ2, ..., λn) ∈ R n iff operator Aη ...
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This paper studies the H∞ control of infinitedimensional systems whose transfer matrices are expressible as a series connection of a rational transfer matrix and a scalar (possibly irrational) inner function. This class of systems is adequate for describing many control problems in practice, when weighting functions are rational and plants have at most finitely many unstable modes. We show that...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1997
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-73-1-35-65