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Some Remarks on Shanks-type Conjectures
Published 3 May 2024 in math.CV and math.FA | (2405.02405v1)
Abstract: We discuss the zero sets of two-variable polynomials as they relate to an approximation problem in the Hardy space on the bidisk.
- C. Bénéteau and R. Centner. A survey of optimal polynomial approximants, applications to digital filter design, and related open problems. Complex Anal. Synerg., 7(2):Paper No. 16, 12, 2021.
- Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants. J. Lond. Math. Soc. (2), 94(3):726–746, 2016.
- C. Felder. General optimal polynomial approximants, stabilization, and projections of unity. Anal. Theory Appl., 39(4):309–329, 2023.
- Y. Genin and Y. Kamp. Counterexample in the least-squares inverse stabilisation of 2d recursive filters. Electronics Letters, 11(15):330 – 331, 1975.
- Y. Genin and Y. Kamp. Two-dimensional stability and orthogonal polynomials on the hypercircle. Proceedings of the IEEE, 65(6):873–881, 1977.
- Stable and real-zero polynomials in two variables. Multidimens. Syst. Signal Process., 27(1):1–26, 2016.
- W. Rudin. Function theory in polydiscs. W. A. Benjamin, Inc., New York-Amsterdam, 1969.
- M. Sargent and A. A. Sola. Optimal approximants and orthogonal polynomials in several variables II: Families of polynomials in the unit ball. Proc. Amer. Math. Soc., 149(12):5321–5330, 2021.
- M. Sargent and A. A. Sola. Optimal approximants and orthogonal polynomials in several variables. Canad. J. Math., 74(2):428–456, 2022.
- Stability and synthesis of two-dimensional recursive filters. IEEE Transactions on Audio and Electroacoustics, 20(2):115–128, 1972.
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