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Frame Properties of Shifts of Prolate and Bandpass Prolate Functions

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Frames and Other Bases in Abstract and Function Spaces

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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Abstract

Frame properties of shifts of certain prolate spheroidal wave functions and corresponding bandpass prolates are reviewed and analogues between continuous and finite dimensional theories are pointed out. An application to the study of phase locking in electroencephalography channel signals is also reviewed.

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Acknowledgements

The authors would like to thank both anonymous referees for several helpful suggestions.

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Authors and Affiliations

  1. School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW, 2308, Australia

    Jeffrey A. Hogan

  2. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003-8001, USA

    Joseph D. Lakey

Authors
  1. Jeffrey A. Hogan
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  2. Joseph D. Lakey
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Correspondence to Jeffrey A. Hogan .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Temple University, Philadelphia, Pennsylvania, USA

    Isaac Pesenson

  2. School of Mathematics and Statistics, The University of New South Wales, Sydney, New South Wales, Australia

    Quoc Thong Le Gia

  3. Department of Mathematics, The Graduate Center, CUNY, New York, New York, USA

    Azita Mayeli

  4. Institute of Mathematical Sciences, Claremont Graduate University, Claremont, California, USA

    Hrushikesh Mhaskar

  5. Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong

    Ding-Xuan Zhou

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Hogan, J.A., Lakey, J.D. (2017). Frame Properties of Shifts of Prolate and Bandpass Prolate Functions. In: Pesenson, I., Le Gia, Q., Mayeli, A., Mhaskar, H., Zhou, DX. (eds) Frames and Other Bases in Abstract and Function Spaces. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55550-8_10

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