An Inequality for Trigonometric Polynomials

• Autorzy: Govil N. K. , Qazi M. A. , Rahman Q. I.

Identyfikatory

DOI

10.4064/ba60-3-4

• Języki publikacji: EN

Abstrakty

EN

The main result says in particular that if t(ζ):=∑..[formula] is a trigonometric polynomial of degree n having all its zeros in the open upper half-plane such that |t(ξ)|≥μ on the real axis and cn/=0, then |t′(ξ)|≥μn for all real ξ.

Słowa kluczowe

EN

polynomials; Laurent polynomial; Bernstein’s inequality; minimum modulus

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: Vol. 60, no 3
• Strony: 241--247
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Govil N. K.

• Department of Mathematics Auburn University Auburn, AL 36849-5310, U.S.A.

autor

Qazi M. A.

• Department of Mathematics Tuskegee University Tuskegee, AL 36088, U.S.A.

autor

Rahman Q. I.

• Département de Mathématiques et de Statistique Université de Montréal Montréal, H3C 3J7, Canada

Bibliografia

• [1] L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. ed., Reidel, Dordrecht, 1974.
• [2] C. Jordan, Calculus of Finite Differences, 3rd ed., Chelsea, New York, 1965.
• [3] Q. I. Rahman and G. Schmeisser, Analytic Theory of Polynomials, Clarendon Press, Oxford, 2002.