The Bessel Wavelet Transform

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 at the Department of Mathematical Sciences at the Indian Institute of Technology (Banaras Hindu University), Varanasi, Uttar Pradesh, India. With more than 27 years of research and teaching experience, his areas of research interest are distribution theory, pseudo-differential operators, and wavelet analysis. With more than 100 papers published in various national and international journals, he has delivered many lectures in national and international conferences, workshops and training programs in India and abroad.

Jay Singh Maurya is Assistant Professor at the Department of Mathematical Sciences at Galgotia University, Greater Noida, Gautam Buddha Nagar, Uttar Pradesh, India. He has done Ph.D. in Mathematics at the Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi, Uttar Pradesh, India, in 2022, and M.Sc. (Mathematics) from the India Institute of Technology Kanpur, Uttar Pradesh, India. His area of specialization is wavelet analysis, distribution theory, applied harmonic analysis and microlocal analysis. He has devised the construction of the wavelet inversion formula and its associated results on various functional spaces.

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.