RUS  ENG
Full version
JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2021 Volume 499, Pages 53–66 (Mi znsl7044)

I

Refinement masks of tight wavelet frames

E. A. Lebedeva, I. A. Sherbakov

St. Petersburg State University, Mathematics and Mechanics Faculty

Abstract: In the paper we obtain sufficient conditions for a trigonometric polynomial to be a refinement mask corresponding to a tight wavelet frame. The condition is formulated in terms of the roots of a mask. In particular, it is proved that any trigonometric polynomial can serve as a mask if its associated algebraic polynomial has only nonpositive roots (at least one of them, of course, equals $-1$).

Key words and phrases: refinement masks, elementary symmetric polynomials, tight wavelet frames.

UDC: 517.5

Received: 28.10.2020



© Steklov Math. Inst. of RAS, 2025