Wavelet Analysis on Local Fields of Positive Characteristic

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.

“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)

• 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.