Integral Equations and Operator Theory

, Volume 68, Issue 2, pp 163–191 | Cite as

Discrete-Time Multi-Scale Systems



We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the polydisc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier.

Mathematics Subject Classification (2000)

Primary 94A12 47N70 46E22 Secondary 93D25 42A70 


Discrete-scale transformation scale invariance linear systems self-similarity reproducing kernels 


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© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of mathematicsBen-Gurion University of the NegevBeershebaIsrael
  2. 2.CReSTIC-UFR des Sciences Exactes et NaturellesUniversité de Reims Champagne-ArdenneReims Cedex 2France

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