Re: OPs in the class M

[thk (Tom H. Koornwinder)]

I forward the folling message from Thomas Dehn to OP-SF NET.
Tom Koornwinder
--------------------------------------------

> Topic #3   -------------   OP-SF NET 5.2  ------------  March 15, 1998
>                            ~~~~~~~~~~~~~
> From: OP-SF NET  Editor <muldoon@yorku.ca>
> Subject: From opsftalk
>
> Recent enquiries in opsftalk include the following query from Paul Nevai:
>
> "Is this new (I hope)?  If the measure is in the class M then there are
> finitely many masspoints greater than 1 if and only if the ratio of the
> consecutive ops evaluated at the point 1 converges to 1."

If I don't miss something (I work in a different area right
now), I proved the above result in 1991, and it is contained
both in my PhD thesis (which is written in German)
and in my paper "A shortcut to asymptotics for
orthogonal polynomials" (Theorem 8 in section 4.1 and
the remark after the proof).
published in J. Comp. and Appl. Math. in 1994.


Thomas Dehn
dehn@ipmsun5.mathematik.uni-karlsruhe.de
or
thomas.dehn@bgr.de (will be invalid after Jul 31st 1998).