Ahmed I. Zayed,Handbook of Function and GeneralizedFunction Transformations

✍ Scribed by S.B. Yakubovich

• Book ID: 102579413
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 158 KB
• Volume: 90
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1997.3148

✦ Synopsis

In the last chapter (which was written in collaboration with A. Pra staro), the authors return to the d'Alembert equation ( 4), and they make a detailed study of it from the point of view of the modern geometric theory of partial differential equations. This chapter, unlike the earlier ones which require only a background subsumed in the usual graduate course in real analysis, requires more mathematical sophistication. Terms like tensor products, n-dimensional manifolds, tangent bundles, cotangent bundles, the tangent space at a point, fibre bundles, etc., appear in Chapter 8 for the first time. The reader not versed in differential geometry may find the going a little rough here.

The book concludes with a section stating seven open problems. I found this to be a well-written book with a unified approach to a subject whose main results had heretofore only been located in journal articles and unpublished manuscripts. I can heartily recommend it to anyone who is interested in knowing when a function of many variables can be represented as the sum of a product of functions of single variables.