This book is a collated form of the lectures given in a series of events titled “Advanced Functional Analysis and its Applications” conducted at Indian Institute of Technology Hyderabad between years 2019 to 2024. These winter schools focused on various developments on the aforesaid topic. This book is intended to serve the purpose of adding to the knowledge of researchers who are working in Functional Analysis or its allied fields. Additionally, these highlight material that is not included in a typical Functional Analysis or Operator Theory course, but which, if understood, would bring a better level of maturity to those areas. This book serves as a refresher course for college lecturers interested in learning the current developments of Mathematical Analysis. We express our gratitude to our sponsors for their endorsement of the funding for these workshops. We have secured funding from TEQIP MHRD, NBHM, ANRF, as well as from IIT Hyderabad. Finally, each of the lecturers of these workshops have consciously stepped forward to contribute to the success of each and every event. This book is a result of the joint efforts of all those delegates.
About the Author :
S. Kesavan received his Docteur-es-Sciences Mathematiques from the Universite Pierre et Marie Curie (Paris VI) in 1979 for the thesis entitled Sur l'approximation de probl`emes lineaires et nonlineaires de valeurs propres, supervised by Professors J.L. Lions and P.G. Ciarlet. Earlier, he served as Professor at the Institute of Mathematical Sciences, Chennai, India, and Deputy Director at Chennai Mathematical Institute, India. His research areas include partial differential equations, homogenization, control theory, and isoperimetric inequalities. Author of 5 books, Prof. Kesavan has published over 50 papers in national and international journals in addition to several contributions to conference proceedings. He was elected Vice-President of the Ramanujan Mathematical Society in 2019 and Fellow of the Indian Academy of Sciences, Bangalore, in 2008.
Gadadhar Misra is Visiting Professor in the Department of Mathematics, the Indian Institute of Technology Gandhinagar, Gujarat, India. Earlier, he has been Chairman and Professor in the Department of Mathematics, the Indian Institute of Science (IISc), Bengaluru, Karnataka, India. He was also Head of the Indian Statistical Institute, Bangalore, Karnataka, India. A distinguished mathematician, a brilliant teacher and an active researcher, he held several key positions: member of the National Board of Higher Mathematics; Co-convener of the KVPY and the Indian Academy of Sciences (2007-2009). He is the Fellow of the Indian Academy of Sciences, the Indian National Science Academy, the National Academy of Sciences and a recipient of J.C. Fellowship. His research interests lie in operator theory, functional analysis and Hilbert modules. He has been contributing significantly to promoting collaborative research and strengthening mathematical education in India.
Tanmoy Paul is Associate Professor in the Department of Mathematics, IIT Hyderabad, Telangana, India. He completed his Ph.D. on the topic "functional analysis, analysis on Banach spaces" from the ISI Kolkata. His current area of interest is functional analysis, Banach space theory, convex analysis and geometric measure theory.
T.S.S.R.K. Rao is Distinguished Professor in the Department of Mathematics, Shiv Nadar University, Gautam Buddha Nagar, Uttar Pradesh, India. Earlier, he was Professor and Head of the Theoretical Statistics and Mathematics Division, ISI Bangalore, Karnataka, Bengaluru, India. He is one of the eminent experts in functional analysts in India. He worked in various domains like approximation theory, analysis on Banach spaces and their geometry, Choquet theory and optimization techniques.
