Acta mathematica scientia,Series A ›› 1997, Vol. 17 ›› Issue (S1): 132-139.

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ORTHONORMAL POLYNOMIAL BASSES AND WAVELET-PACKETS

Han Bin   

  1. Institute of Mathematics, Academia Sinica, Beijing 100080, China and Dept. of Mathematics, University of Alberta, Edmonton T6G 2G1. Canada
  • Received:1994-08-05 Revised:1996-11-08 Online:1997-12-26 Published:1997-12-26

Abstract: 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.

Key words: Trigonometric polynomial bases, wavelets, best approximation

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