Completeness And Basic Properties Of Sets Of Special Functions

Completeness and Basis Properties of Sets of Special Functions

Presents methods for testing sets of special functions for completeness and basis properties, mostly in L2 and L2 spaces.

Completeness and basic properties of sets of special functions

Theory and Applications of Special Functions

This volume, "Theory and Applications of Special Functions," is d- icated to Mizan Rahman in honoring him for the many important c- tributions to the theory of special functions that he has made over the years, and still continues to make. Some of the papers were presented at a special session of the American Mathematical Society Annual Meeting in Baltimore, Maryland, in January 2003 organized by Mourad Ismail. Mizan Rahman's contributions are not only contained in his own - pers, but also indirectly in other papers for which he supplied useful and often essential information. We refer to the paper on his mathematics in this volume for more information. This paper contains some personal recollections and tries to describe Mizan Rahman's literary writings in his mother tongue, Bengali. An even more personal paper on Mizan Rahman is the letter by his sons, whom we thank for allowing us to reproduce it in this book. The theory of special functions is very much an application driven field of mathematics. This is a very old field, dating back to the 18th century when physicists and mathematician were looking for solutions of the fundamental differential equations of mathematical physics. Since then the field has grown enormously, and this book reflects only part of the known applications.