@article{0d995149134d4d3cbdb999341ad0fb5d,
title = "FACTORIZATION OF SINGULAR MATRIX POLYNOMIALS AND MATRICES WITH CIRCULAR HIGHER RANK NUMERICAL RANGES",
abstract = "Factorization of regular Hermitian valued trigonometric polynomials (on the unit circle) and Hermitian valued polynomials (on the real line) have been studied well. In this paper we drop the condition of regularity and study factorization of singular Hermitian valued (trigonometric) polynomials. We subsequently apply the results to obtain a characterization of matrices with a circular higher rank numerical range and derive a new version of Anderson's theorem. As a special case, we obtain a new characterization of matrices with a circular numerical range.",
keywords = "Hermitian valued trigonometric polynomials, J-spectral factorization, circular numerical range, higher rank numerical range",
author = "Edward Poon and Spitkovsky, {Ilya M.} and Woerdeman, {Hugo J.}",
note = "Funding Information: \ast Received by the editors February 4, 2022; accepted for publication (in revised form) by B. Meini May 31, 2022; published electronically August 18, 2022. https://doi.org/10.1137/22M1475934 Funding: The work of the second author was partially supported by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi. The work of the third author was supported by the Simons Foundation grant 355645 and the National Science Foundation grant DMS-2000037. \dagger Department of Mathematics, Embry--Riddle Aeronautical University, Prescott, AZ 86301 USA (
[email protected]). \ddagger Division of Science and Mathematics, New York University Abu Dhabi (NYUAD), Saadiyat Island, Abu Dhabi, UAE (
[email protected]). \S Department of Mathematics, Drexel University, Philadelphia, PA 19104 USA (hugo@math. drexel.edu). Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",
year = "2022",
doi = "10.1137/22M1475934",
language = "English (US)",
volume = "43",
pages = "1423--1439",
journal = "SIAM Journal on Matrix Analysis and Applications",
issn = "0895-4798",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}