Wavelet Analysis on Local Fields of Positive Characteristic

Biswaranjan Behera, Qaiser Jahan

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English

Springer Verlag, Singapore
19 December 2022

Calculus & mathematical analysis; Complex analysis, complex variables; Functional analysis & transforms

Series: Indian Statistical Institute Series

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.

By: Biswaranjan Behera, Qaiser Jahan
Imprint: Springer Verlag, Singapore
Country of Publication: Singapore
Edition: 2021 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 539g
ISBN: 9789811678837
ISBN 10: 9811678839
Series: Indian Statistical Institute Series
Pages: 333
Publication Date: 19 December 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Local Fields.- Multiresolution Analysis on Local Fields.- Aﬃne, Quasi-Aﬃne and Co-Aﬃne Frames.- Characterizations in Wavelet Analysis.- Biorthogonal Wavelets.- Wavelet Packets and Frame Packets.- Wavelets as Unconditional Bases.- Shift-Invariant Spaces and Wavelets.

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.

Reviews for Wavelet Analysis on Local Fields of Positive Characteristic

“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)