Establish nonvanishing of the leading amplitude in the orthorecursive expansion

Establish the nonvanishing of the leading amplitude governing the decay of the partial sums in the orthorecursive expansion of unity, in order to determine whether the presently obtained decay estimates are optimal.

Background

The monograph applies its arithmetic-kernel framework to the orthorecursive expansion of unity associated with Kalmynin and Kosenko. It improves the known decay estimates and develops an associated spectral description, but does not prove that the leading asymptotic amplitude is nonzero. Such nonvanishing is needed to establish full optimality of the decay rate.