Hurwitz matrices of doubly infinite series

DOI10.1016/j.laa.2017.05.012zbMath1371.30002arXiv1608.04440OpenAlexW2508418100MaRDI QIDQ2013191

Alexander Dyachenko

Publication date: 3 August 2017

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.04440

zbMATH Keywords

Pólya frequency sequencetotal positivitygeneralized Hurwitz matrixHurwitz matrixdoubly infinite series

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Positive matrices and their generalizations; cones of matrices (15B48) Power series (including lacunary series) in one complex variable (30B10) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15)

Cites Work

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• Generalized Hurwitz matrices, generalized Euclidean algorithm, and forbidden sectors of the complex plane
• On totally positive sequences and functions
• Total nonnegativity of infinite Hurwitz matrices of entire and meromorphic functions
• Structured Matrices, Continued Fractions, and Root Localization of Polynomials
• A Hurwitz Matrix is Totally Positive
• 𝑅-functions—analytic functions mapping the upper halfplane into itself
• Zeros of Reliability Polynomials and f-vectors of Matroids
• On the Total Nonnegativity of the Hurwitz Matrix
• On the Generating Functions of Totally Positive Sequences
• On the Generating Function of a Doubly Infinite, Totally Positive Sequence

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