Asymptotic expansion of norm associated with conjugate trigonometric polynomial. (English) Zbl 0791.41029
Summary: Let \(T_ n(x)\) be a trigonometric polynomial of degree \(n\), and \(\widetilde T_ n(x)\) be the conjugation of \(T_ n(x)\). We obtain the complete asymptotic expansion for \(C_ n=\sup_{\| T_ n\|_ C\leq 1} \|\widetilde T_ n\|_ C\) for \(n\to\infty\).
MSC:
41A60 | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) |
42A05 | Trigonometric polynomials, inequalities, extremal problems |
References:
[1] | A. Zygmund,Trigonometric Series, Vol.1 and2, Cambridge University Press, 1959. · Zbl 0085.05601 |
[2] | L. V. Taikov,Math. Notes,48 (1990), 110–114. |
[3] | H. Ehlich andK. Zeller,Math. Ann.,164 (1966), 105–112. · Zbl 0136.04604 · doi:10.1007/BF01429047 |
[4] | P. N. Shivakumar andR. Wong,Math. Comput.,39 (1982), 195–200. · doi:10.1090/S0025-5718-1982-0658223-X |
[5] | G. J. Feng,Math. Numer. Sinica,4 (1985), 420–425. |
[6] | I. S. Gradshtenyn andI. M. Ryzhik,Table of Integrals, Series, and Products, Academic Press, New York, 1980. · Zbl 0521.33001 |
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