Functional Analysis and Applications

Metric Spaces and Banach Fixed Point Theorem.- Banach Spaces.- Hilbert Space.- Fundamental Theorems.- Differential and Integral Calculus in Banach Spaces.- Optimisation Problems.- Operator Equations and Variational Methods.- Finite Element and Boundary Element Methods.- Variational Inequalities and Applications.- Spectral Theory with Application.- Frame and Basis Theory in Hilbert Spaces.- Wavelet Theory.- Wavelet Method for Partial Dierential Equations and Image Processing.- Wavelet Frames.- Gabor Analysis.

Abul Hasan Siddiqi is Professor Emeritus and a distinguished scientist at the School of Basic Sciences and Research, Sharda University, Greater Noida, India. Professor Siddiqi has held several important administrative positions, such as Chairman of the Department of Mathematics, Dean of the Faculty of Science, and Pro-Vice-Chancellor of Aligarh Muslim University, India. He has been actively associated with the International Centre for Theoretical Physics, Trieste, Italy (UNESCO organization), in different capacities for more than 20 years. He served as Professor of Mathematics at the King Fahd University of Petroleum and Minerals (KFUPM), Saudi Arabia, for 10 years; and a consultant to Sultan Qaboos University, Oman; Istanbul Aydin University, Turkey; and the Institute of Microelectronics, Malaysia. He was awarded the German Academic Exchange Service (DAAD) Fellowship thrice to pursue mathematical research in Germany. He has jointly published more than 100 research papers with his research collaborators, 5 books, and edited proceedings of 9 international conferences. He is Founder Secretary of the Indian Society of Industrial and Applied Mathematics (ISIAM) and Editor-in-Chief of the Indian Journal of Industrial and Applied Mathematics, published by the ISIAM, and  the Springer book series, Industrial and Applied Mathematics. He has recently been elected as President of ISIAM, which represents India at the apex forum of industrial and applied mathematics—ICIAM.