The coefficient ratio conjecture for complete Nevanlinna–Pick kernels

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Let an}a_n\} and bn}b_n\} be sequences related as in equation (4.1), and suppose that

∑n=1∞bn=1.\sum_{n=1}^\infty b_n=1.

Coefficient ratio conjecture. Then

lim⁡n→∞anan+1=1.\lim_{n\to\infty}\frac{a_n}{a_{n+1}}=1.

This concerns the asymptotic behavior of coefficients defining a radial complete Nevanlinna–Pick kernel. The supplied text does not state whether the claim has been proved or disproved.

References

Primary source

Devin Greene, Stefan Richter and Carl Sundberg, “The Structure of Inner Multipliers on Spaces with Complete Nevanlinna Pick Kernels”, arXiv:math/0108007 (2001).

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