Fourth, for the case n odd, we show that the Second Regularity Hypothesis
For Odd Order Case [6, p. 2337] is a direct consequence of the First Regularity
Hypothesis For Odd Order Case [6, p. 2336], thereby improving the results in .
We also make a slight improvement in the Regularity Hypothesis For Even Order
Case [6, p. 2322]. For the case n even, we employ only one basis and one sector of
angular opening 2n/n, so the theory does not have to be worked out twice on two
different sectors of angular opening ir/n.
Acknowledgments. I would like to take this opportunity to thank my friend
and coauthor, Patrick Lang, for his many contributions to our joint work over the
last seventeen years. His inspiration and hard work have had a profound influence
on this monograph. And to my wife Georgia, my companion and friend of forty
years, I express my sincerest thanks and gratitude. Your patience, positive attitude,
and words of encouragement have made this book possible.