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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Low-pass filters and representations of the Baumslag Solitar group
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by Dorin Ervin Dutkay PDF
Trans. Amer. Math. Soc. 358 (2006), 5271-5291 Request permission

Abstract:

We analyze representations of the Baumslag Solitar group \[ BS(1,N)=\langle u,t | utu^{-1}=t^N\rangle \] that admit wavelets and show how such representations can be constructed from a given low-pass filter. We describe the direct integral decomposition for some examples and derive from it a general criterion for the existence of solutions for scaling equations. As another application, we construct a Fourier transform for some Hausdorff measures.
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Additional Information
  • Dorin Ervin Dutkay
  • Affiliation: Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
  • MR Author ID: 608228
  • Email: ddutkay@math.rutgers.edu
  • Received by editor(s): July 21, 2004
  • Published electronically: July 21, 2006
  • Additional Notes: This work was supported in part by NSF grant DMS0457491
  • © Copyright 2006 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 5271-5291
  • MSC (2000): Primary 42C40, 28A78, 46L45, 28D05, 22D25
  • DOI: https://doi.org/10.1090/S0002-9947-06-04230-9
  • MathSciNet review: 2238916