A new proof and a generalization of a theorem of de Bruijn

Aziz, Abdul

doi:10.1090/S0002-9939-1989-0933511-6

A new proof and a generalization of a theorem of de Bruijn
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Proc. Amer. Math. Soc. 106 (1989), 345-350 Request permission

Abstract:

Using a recently developed interpolation formula, we present elementary new and simple proofs of De Bruijn’s theorem and Zygmund’s inequality concerning the integral mean estimates for polynomials. We also present a generalization of De Bruijn’s theorem which leads to a refinement of a theorem of Erdös and Lax.

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A remark on conjugate series

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