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Wavelet Analysis on Local Fields of Positive Characteristic

  • Book
  • © 2021

Overview

Authors:
  1. Biswaranjan Behera

    1. Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata, India

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  2. Qaiser Jahan

    1. School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, India

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  • Discusses, for the first time, wavelet analysis on local fields of positive characteristic
  • Provides a proof of the existence and uniqueness of Haar measures on locally compact groups
  • Focuses on multiresolution analysis and wavelets on a local field of positive characteristic

Part of the book series: Indian Statistical Institute Series (INSIS)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xvii
    Download chapter PDF

  2. Local Fields

    • Biswaranjan Behera, Qaiser Jahan
    Pages 1-84

  3. Multiresolution Analysis on Local Fields

    • Biswaranjan Behera, Qaiser Jahan
    Pages 85-129

  4. Affine, Quasi-affine and Co-affine Frames

    • Biswaranjan Behera, Qaiser Jahan
    Pages 131-160

  5. Characterizations of Functions Associated with Wavelet Analysis

    • Biswaranjan Behera, Qaiser Jahan
    Pages 161-221

  6. Biorthogonal Wavelets

    • Biswaranjan Behera, Qaiser Jahan
    Pages 223-244

  7. Wavelet Packets and Frame Packets

    • Biswaranjan Behera, Qaiser Jahan
    Pages 245-267

  8. Wavelets as Unconditional Bases

    • Biswaranjan Behera, Qaiser Jahan
    Pages 269-300

  9. Shift-Invariant Spaces and Wavelets

    • Biswaranjan Behera, Qaiser Jahan
    Pages 301-330

  10. Back Matter

    Pages 331-333
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Keywords

About this book

This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces. 

Reviews

“The book provides the first systematic account of wavelets on local fields, and the authors give a clear presentation of the topics discussed.” (Krishnan Parthasarathy, Mathematical Reviews, April, 2023)

Authors and Affiliations

  • Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata, India

    Biswaranjan Behera

  • School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, India

    Qaiser Jahan

About the authors

BISWARANJAN BEHERA is Associate Professor at the Statistics and Mathematics Unit of the Indian Statistical Institute (ISI), Kolkata, India. He received his M.Sc. degree in Mathematics from Sambalpur University, Odisha, India, in 1992, and the Ph.D. degree from the Indian Institute of Technology (IIT) Kanpur, India, in 2001. He was Postdoctoral Fellow at ISI, Kolkata, from 2001–2004. He joined IIT Delhi as Assistant Professor, in 2004. He is working at ISI, Kolkata, since 2010. His research interests are wavelet analysis on the Euclidean spaces, Hardy space and local fields of positive characteristic, and weighted norm inequalities on local fields. 


QAISER JAHAN is Assistant Professor at the Indian Institute of Technology (IIT) Mandi, India. She received her M.Sc. degree in Mathematics from the University of Allahabad, India, in 2006, and her Ph.D. from the Indian Statistical Institute, Kolkata, in 2014. After her Ph.D., she worked as Visiting Scientist at ISI, Kolkata, and as Postdoctoral Fellow at IIT Kanpur for two years. After that, she joined the Indian Institute of Science (IISc), Bangalore, as Kothari Postdoctoral Fellow. She has visited a few institutes in abroad for research purposes like the University of Oregon, USA; Philipps University, Germany; and the Institute of Mathematics, the Polish Academy of Sciences. She was awarded the Indo-US WISTEMM fellowship. Her research area is harmonic analysis. In particular, she is working on wavelet analysis, local fields, coorbit spaces, shearlet coorbit spaces, etc. She has written eight research articles in international journals and one conference paper in SampTA 2019.

Bibliographic Information

  • Book Title: Wavelet Analysis on Local Fields of Positive Characteristic

  • Authors: Biswaranjan Behera, Qaiser Jahan

  • Series Title: Indian Statistical Institute Series

  • DOI: https://doi.org/10.1007/978-981-16-7881-3

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021

  • Hardcover ISBN: 978-981-16-7880-6Published: 18 December 2021

  • Softcover ISBN: 978-981-16-7883-7Published: 19 December 2022

  • eBook ISBN: 978-981-16-7881-3Published: 01 January 2022

  • Series ISSN: 2523-3114

  • Series E-ISSN: 2523-3122

  • Edition Number: 1

  • Number of Pages: XVII, 333

  • Topics: Abstract Harmonic Analysis, Fourier Analysis, Analysis

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