Functional analysis and transforms

The present work is an extended version of a manuscript of a course which the author taught at the University of Hamburg during summer 1969.

The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021.

This book, the second of two volumes, presents significant applications for understanding modern analysis.

The book is devoted to the study of approximate solutions of fixed point problems in the presence of computational errors.

Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2.

In this book, there is a strong emphasis on application with the necessary mathematical grounding.

Large numbers of studies of the KdV equation have appeared since the pioneering paper by Gardner, Greene, Kruskal, and Miura in 1967.

This is an invaluable book that presents the original work published in French, in 1904, by Henry Leon Lebesgue, the creator of the theory of integration.

The book discusses important results in modern mathematical models and high performance computing, such as applied operations research, simulation of operations, statistical modeling and applications, invisibility regions and regular meta-materials, unmanned vehicles, modern radar techniques/SAR imaging, satellite remote sensing, coding, and robotic systems.

This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces.

The real-variable theory of function spaces has always been at the core of harmonic analysis.