This book presents the theory of Bessel wavelet transformation involving Hankel transformation. Several properties of the Bessel wavelet transform are discussed in the classical and distributional sense. Other related results of Hankel transform, Hankel convolution and basic results of distributions are also explained. Throughout the book, the reader is assumed to have an understanding of the elements of analysis. Introductory chapters cover the prerequisites for distribution theory. This book is useful for graduate students and researchers in mathematics, physics, engineering and applied sciences.

Discusses the theory of wavelet transformation involving Hankel transformation Presents the Bessel wavelet transform in the classical as well as in the distributional sense Targets graduate students and researchers in mathematics, physics, engineering, and applied sciences

Autorentext

Santosh Kumar Upadhyay is Professor in the Department of Mathematical Sciences, Indian Institute of Technology Varanasi (Banaras Hindu University) (IIT-BHU), Varanasi, Uttar Pradesh, India. His area of specialization is functional analysis, pseudo-differential operators, and wavelet analysis. With more than 100 papers published in various national and international journals, he has delivered many lectures in several national/international conferences, workshops, and training programs in India and abroad. He has more than 29 years of teaching experience in various institutions of repute in India. Mohd Sartaj is Assistant Professor in the Department of Basic Sciences and Humanities, PSIT Kanpur, Uttar Pradesh, India. Earlier, he was Research Scholar in the Department of Mathematical Sciences, Indian Institute of Technology Varanasi (Banaras Hindu University) (IIT-BHU), Varanasi, Uttar Pradesh, India, from January 2019 to October 2023. He completed his Ph.D. degree from the IIT-BHU, in 2024. His area of specialization is pseudo-differential operators and distribution theory. He published several papers in various national and international journals.

Inhalt

An Overview.- On Continuous Bessel Wavelet Transformation Associated with the Hankel-Hausdorff Operator.- Bessel Wavelet Transform on the Spaces with Exponential Growth.- The Bessel Wavelet Convolution Product.- The Relation Between Bessel Wavelet Convolution Product and Hankel Convolution Product Involving Hankel Transform.- Integrability of the Continuum Bessel Wavelet Kernel.- Continuous Bessel Wavelet Transform of Distributions.- Characterizations of the Bessel Wavelet Transform in Besov and Triebel-Lizorkin Type Spaces.- Characterizations of the Inversion Formula of the Continuous Bessel Wavelet Transform of Distributions in.- The Continuous Bessel Wavelet Transform of Distributions in 𝜷 𝝁-Space.- The Bessel wavelet transform of distributions in 𝑯𝝁,2 space.