Journal article
The autoregressive filter problem for multivariable degree one symmetric polynomials
Acta scientiarum mathematicarum (Szeged), v 89(3-4), pp 509-532
01 Nov 2023
Abstract
The multivariable autoregressive filter problem asks for a polynomial p(z) = p(z(1), ... , z(d)) without roots in the closed d-disk based on prescribed Fourier coefficients of its spectral density function 1/|p(z)|(2). 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 F-2(1) ((1/3, 2/3)(1); z) and F-2(1 )((1/2,1/2 )(1); (sic))
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Details
- Title
- The autoregressive filter problem for multivariable degree one symmetric polynomials
- Creators
- Jeffrey S. Geronimo - Georgia Institute of TechnologyHugo J. Woerdeman - Drexel University, MathematicsChung Y. Wong - Cty Coll Morris, Dept Math, 214 Ctr Grove Rd, Randolph, NJ 07869 USA
- Publication Details
- Acta scientiarum mathematicarum (Szeged), v 89(3-4), pp 509-532
- Publisher
- Springer Nature
- Number of pages
- 24
- Grant note
- DMS 2000037 / National Science Foundation; National Science Foundation (NSF) 355645 / Simons Foundation
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000943276400001
- Scopus ID
- 2-s2.0-85149254028
- Other Identifier
- 991021861295804721
InCites Highlights
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics