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The Path to Λ-Bounded variation

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Recent Advances in Harmonic Analysis and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 25))

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Abstract

This is a personal account describing the evolution of the concept of Λ-bounded variation. Earlier generalizations of bounded variation are described. A test for the convergence of Fourier series due to Salem was pivotal, leading to a condition for preservation of convergence of Fourier series under change of variable and, finally, to a new notion of bounded variation. Some applications and generalizations to higher dimensions are indicated.

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Authors and Affiliations

  1. Syracuse University and Florida Atlantic University, 7739 Majestic Palm Drive, Boynton Beach, FL, 33437, USA

    Daniel Waterman

Authors
  1. Daniel Waterman
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Correspondence to Daniel Waterman .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of South Carolina, Greene Street 1523, Columbia, 29208, South Carolina, USA

    Dmitriy Bilyk

  2. University Park, Department of Mathematics, Florida International University, SW 8th St., Rm 416 11200, Miami, 33199, Florida, USA

    Laura De Carli

  3. , Department of Mathematics, Universtity of Georgia, University of Georgia, Athens, 30602, Georgia, USA

    Alexander Petukhov

  4. Georgia Southern University, PO Box 8093, Statesboro, 30460, Georgia, USA

    Alexander M. Stokolos

  5. , Department of Mathematics, Georgia Institute of Technology, Cherry Street 686, Atlanta, 30332, Georgia, USA

    Brett D. Wick

Additional information

Dedicated to the memory of Casper Goffman, my friend, colleague, and coworker

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Waterman, D. (2012). The Path to Λ-Bounded variation. In: Bilyk, D., De Carli, L., Petukhov, A., Stokolos, A., Wick, B. (eds) Recent Advances in Harmonic Analysis and Applications. Springer Proceedings in Mathematics & Statistics, vol 25. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4565-4_29

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