Pseudo-Differential Operators and the Weinstein Transform

This book discusses topics on the Fourier transform, Hankel transform, Weinstein transform, and pseudo-differential operators. Targeted to researchers and graduate students, it is useful in the study of the theory of pseudo-differential operators involving the Weinstein transform. This book is also helpful in the study of partial differential equations, wavelet analysis, harmonic analysis, and functional analysis. Throughout the book, the reader is assumed to have an understanding of the basics of real analysis and functional analysis. The Weinstein transform whose kernel consists of a complex exponential function and a normalized Bessel function of the first kind. The Weinstein transform has a rich calculus and can be applied in many areas of mathematical sciences. Pseudo-differential operators are the generalization of partial differential operators, and they play a significant role in the problems of partial differential equations, numerical analysis, and quantum physics.

The Fourier Transform.- Pseudo-Differential Operators involving the Fourier Transform.- The Hankel Transform.- The Weinstein Transform.- Pseudo-Differential Operators involving the Weinstein transform.- Pseudo-Differential Operators of Homogeneous symbol classinvolving the Weinstein transform.- Boundedness of Pseudo-Differential Operators involvingthe Weinstein transform.- Symmetrically Global Pseudo-Differential Operators involving theWeinstein transform.- Composition of Pseudo-Differential Operators involving theWeinstein transform.

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.