Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/86109
Authors: 
Protassov, Vladimir
Year of Publication: 
2001
Series/Report no.: 
Tinbergen Institute Discussion Paper 01-046/4
Abstract: 
We consider infinite products of the form ,where {mk} is an arbitrary sequence of trigonometric polynomials of degree at most n with uniformly bounded normssuch that mk(0)=1 for all k. We show that can decrease at infinity not faster than and present conditions underwhich this maximal decay attains. This result proves the impossibility of the construction of infinitely differentiablenonstationary wavelets with compact support and restricts the smoothness of nonstationary wavelets by thelength of their support. Also this generalizes well-known similar results obtained for stable sequences ofpolynomials (when all mk coincide). In several examples we show that by weakening the boundedness conditionsone can achieve an exponential decay.
Subjects: 
trigonometric polynomial
infinite product
wavelets
roots
Document Type: 
Working Paper

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