On the Four Conjectures of G G Lorentz Type in Lρ2[−a, a]

Chinese Quarterly Journal of Mathematics ›› 2009, Vol. 24 ›› Issue (3): 343-348.

On the Four Conjectures of G G Lorentz Type in Lρ²[−a, a]

1. Department of Mathematics, Zhejiang Normal University2. Department of Mathematics, Shanghai Normal University

Received:2005-12-15 Online:2009-09-30 Published:2023-06-27
About author:WANG Yuan-heng(1961- ), mail, native of Nanyang, Henan, a professor of Zhejiang Normal University, M.S.D., engages in functional analysis; YANG Wen-shan(1944- ), native of Taizhou, Zhejiang, a professor of Zhejiang Normal University, M.S.D., engages in approximation theory.
Supported by:
Supported by the NNSF of China(10771141)；

Abstract

Abstract: In the space C[-1,1], G G Lorentz proposed four conjectures on the properties of the polynomials of the best approximation in 1977,1978 and 1980. The present paper transplants the four conjectures in the space L_ρ²[-a,a] and proves them being all right in only one theorem under the corresponding conditions, although each of the original conjectures is very difficulty.

Key words: best approximation, Lorentz’s conjecture, different norms, property of polynomial

CLC Number:

O174.41

WANG Yuan-heng, YANG Wen-shan. On the Four Conjectures of G G Lorentz Type in Lρ²[−a, a] [J]. Chinese Quarterly Journal of Mathematics, 2009, 24(3): 343-348.

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On the Four Conjectures of G G Lorentz Type in Lρ²[−a, a]

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