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Discrete-Time Multi-Scale Systems

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Abstract

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.

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Authors and Affiliations

  1. Department of mathematics, Ben-Gurion University of the Negev, POB 653, 84105, Beersheba, Israel

    Daniel Alpay

  2. CReSTIC-UFR des Sciences Exactes et Naturelles, Université de Reims Champagne-Ardenne, BP 1039, Moulin de la Housse, 51687, Reims Cedex 2, France

    Mamadou Mboup

Authors
  1. Daniel Alpay
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  2. Mamadou Mboup
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Correspondence to Daniel Alpay.

Additional information

D. Alpay thanks the Earl Katz family for endowing the chair which supported his research. This research is part of the European Science Foundation Networking Program HCAA, and was supported in part by the Israel Science Foundation grant 1023/07.

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Alpay, D., Mboup, M. Discrete-Time Multi-Scale Systems. Integr. Equ. Oper. Theory 68, 163–191 (2010). https://doi.org/10.1007/s00020-010-1785-8

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