Wavelet Analysis on Local Fields of Positive Characteristic

by Biswaranjan Behera, Qaiser Jahan

Overview

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. 

Product Details

ISBN-13:	9789811678813
Publisher:	Springer-Verlag New York, LLC
Publication date:	01/01/2022
Series:	Indian Statistical Institute Series
Sold by:	Barnes & Noble
Format:	eBook
File size:	43 MB
Note:	This product may take a few minutes to download.

About the Author

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.

Table of Contents

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.

Editorial 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)

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