The autoregressive filter problem for multivariable degree one symmetric polynomials
The autoregressive filter problem for multivariable degree one symmetric polynomials
复制标题
多元一阶对称多项式的自回归滤波问题
DOI：
10.1007/s44146-023-00072-z
复制
发表时间：
2023
影响因子：
0.5
通讯作者：
Wong, Chung Y.
中科院分区：
文献类型：
--
作者：
Geronimo, Jeffrey S.;Woerdeman, Hugo J.;Wong, Chung Y.
The multivariable autoregressive filter problem asks for a polynomialwithout roots in the closedd-disk based on prescribed Fourier coefficients of its spectral density function. The conditions derived in this paper for the construction of a degree one symmetric polynomial reveal a major divide between the case of at most two variables vs. the the case of three or more variables. The latter involves multivariable elliptic functions, while the former (due to [Geronimo and Woerdeman (Ann Math 160(3):839-906, 2004)]) only involve polynomials. The three variable case is treated with more detail, and entails hypergeometric functions. Along the way, we identify a seemingly new relation between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_2 F_{1}\left( {\frac{1}{3},\frac{2}{3}\atop 1}; \ z\right) $$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_2 F_{1}\left( {\frac{1}{2},\frac{1}{2}\atop 1}; \ \widetilde{z}\right) $$\end{document}.
The multivariable autoregressive filter problem asks for a polynomialwithout roots in the closedd-disk based on prescribed Fourier coefficients of its spectral density function. The conditions derived in this paper for the construction of a degree one symmetric polynomial reveal a major divide between the case of at most two variables vs. the the case of three or more variables. The latter involves multivariable elliptic functions, while the former (due to [Geronimo and Woerdeman (Ann Math 160(3):839-906, 2004)]) only involve polynomials. The three variable case is treated with more detail, and entails hypergeometric functions. Along the way, we identify a seemingly new relation between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_2 F_{1}\left( {\frac{1}{3},\frac{2}{3}\atop 1}; \ z\right) $$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_2 F_{1}\left( {\frac{1}{2},\frac{1}{2}\atop 1}; \ \widetilde{z}\right) $$\end{document}.
登录
查看更多内容
双变量稳定多项式的谱密度函数
DOI：
--
发表时间：
2020
期刊：
The Ramanujan journal
影响因子：
--
作者：
J. Geronimo;H. Woerdeman;Chung Y. Wong
通讯作者：
Chung Y. Wong
多项式求和（Donald Richards 和 Stamatis Cambanis）
影响因子：
10.2
作者：
B. Richmond;C. Rousseau
通讯作者：
C. Rousseau
影响因子：
0.8
作者：
Rosa, Kennett L.;Woerdeman, Hugo J.
通讯作者：
Woerdeman, Hugo J.
用于随机场自回归建模的二维正交晶格结构
影响因子：
5.4
作者：
A. H. Kayran
通讯作者：
A. H. Kayran
DOI：
--
发表时间：
2011
期刊：
影响因子：
--
作者：
M. Bakonyi;H. Woerdeman
通讯作者：
H. Woerdeman