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 |
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