This second edition of Generalized Functions has been strengthened in
many ways. The already extensive set of examples has been expanded.
Since the publication of the first edition, there has been tremendous
growth in the subject and I have attempted to incorporate some of these
new concepts. Accordingly, almost all the chapters have been revised.
The bibliography has been enlarged considerably. Some of the material
has been reorganized. For example, Chapters 12 and 13 of the first
edition have been consolidated into Chapter 12 of this edition by a
judicious process of elimination and addition of the subject matter. The
new Chapter 13 explains the interplay between the theories of moments,
asymptotics, and singular perturbations. Similarly, some sections of
Chapter 15 have been revised and included in earlier chapters to improve
the logical flow of ideas. However, two sections are retained. The
section dealing with the application of the probability theory has been
revised, and I am thankful to Professor Z.L. Crvenkovic for her help.
The new material included in this chapter pertains to the modern topics
of periodic distributions and microlocal theory. I have demonstrated
through various examples that familiarity with the generalized functions
is very helpful for students in physical sciences and technology. For
instance, the reader will realize from Chapter 6 how the generalized
functions have revolutionized the Fourier analysis which is being used
extensively in many fields of scientific activity.
