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- W4246602344 abstract "Let {aℓ(f)}ℓ=−∞∞ be the Fourier coefficients of f∈L[−π,π] and consider the Toeplitz matrices {Tn(f)}, where Tn(f)=(ai−j(f))i,j=1n; thus, {Tn(f)} is generated by the symbol f. There are many results on asymptotic properties of {Tn(f)} as n→∞. If r is a positive integer and Tn(r)(f)=(ar(i−j))i,j=1n, then {Tn(r)(f)}={Tn(fr)} where fr is easily obtained from f. Hence, known results on the asymptotic behavior of Toeplitz matrices generated by a symbol can be applied to {Tn(r)(f)}. Although this is elementary, to our knowledge it has not been previously exploited. We extend this idea to multilevel Toeplitz matrices." @default.
- W4246602344 created "2022-05-12" @default.
- W4246602344 creator A5033668312 @default.
- W4246602344 date "2004-05-01" @default.
- W4246602344 modified "2023-09-27" @default.
- W4246602344 title "An elementary note on asymptotic properties of Toeplitz and multilevel Toeplitz matrices" @default.
- W4246602344 doi "https://doi.org/10.1016/s0024-3795(04)00026-6" @default.
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