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.