数学物理学报 ›› 1997, Vol. 17 ›› Issue (S1): 132-139.
韩斌
Han Bin
摘要： For any fixed ε > 0, an explicit construction of anorthonormal trigonometric polynomial basis {Tk}k=1∞ in L2[0,1) with deg Tk ≤ 0.5(1 +ε)k is presented. Thus weimprove the results obtained by D. Offin and K. Oskolkov in[4] and by Al. A. Privalov in[6]. and practically solve the open problemasked in[4],[8] and[9]. Moreover, as in[4], Fourier sums with respectto this polynomial basis are projectors onto subspaces of trigonometricpolynomials of high degree, which implies almost best approximation-properties.