Introduction to Hyperfunctions and Their Integral Transforms: An Applied and Computational Approach

This textbook presents an introduction to generalized functions through Sato's hyperfunctions, i.e. based on complex variables theory. Laplace transforms, Fourier transforms, Hilbert transforms, Mellin tranforms and Hankel transforms of hyperfunctions and ordinary functions are then treated, and some applications mainly to integral equations are presented. The book is written from an applied and computational point of view and contains many concrete examples.