Tenney Peck, Alex Prestel, Mohan Ramachandran, Ranga Rao, R. M. Robinson, Alex
Rosenberg, Joe Rotman, Olga Taussky-Todd, Nicole Tomczak-Jaegermann, Jerry Uhl,
Lou van den Dries, Doug Vest and Jack Vetzel. Special thanks are due to my
usual collaborators M. D. Choi and T. Y. Lam for many stimulating conversations
about psd and sos forms and to my students William Harris and Julie Simon for
taking time from their dissertations to read various drafts of this paper. I
also thank the referee for a careful and sympathetic reading of the original
manuscript, which led to many clarifications.
At the eleventh hour, my new colleague Zoltan Fiiredi pointed out to me
that, in the presumptively final version of this paper, I had essentially
reinvented the spherical design. I guess I should thank him. Although my
reading of the literature in this subject has delayed publication by several
months, it also led to a tremendous enrichment of sections eight and nine. I
am also grateful to J. J. Seidel, who replied to a desperate letter with a very
patient reply and a bushel of reprints, and to E. Bannai, who clarified some
questions by electronic mail.
Hilda Britt, Kay Daly and Nita McDonald made an excellent translation of
my manuscript into camera-ready form. I thank them for their competence and
their patience.
Finally, the reader will observe that the bibliography is unusually rich
in old research articles. This is a tribute to the magnificent Mathematics
Library at the University of Illinois.
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