Proof of A Conjecture of Iossif Polterovitch that Came Up in the Agmon-Kannai Asymtotic Theory of the Heat Kernel

by Doron Zeilberger

Written: Aug. 11, 2000.

Every mathematician is influenced, directly or indirectly, by every other mathematician. Even in the case of direct influence, there is an explicit and implicit influence, and in the latter case, we are not always aware of it. When I visited my (doctoral) alma mater, The Weizmann Institute of Science, by kind invitation of Amitai Regev, two weeks ago, and met, after many years, my former teacher from grad school, Yakar Kannai (who was also a member of my PhD committee), I realized how much I owe to him. Implicitly, because he was such a great teacher, who taught me PDEs so well, and at the same time how to do mathematics. Explicitly, because he was the first one to tell me about Joseph Bernstein's theory of holonomic systems, that was crucial for so-called WZ theory.

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Added May 24, 2001: Iossif Polterovich has found far-reaching extensions of the method initiated in this note. Read Iossif Polterovich's very interesting paper.

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