The Winding Number at the Critical Hölder Exponent 1/3: Failure of Universal Fourier Summation

Rupert L. Frank, Paata Ivanisvili

The degree (or winding number) of a sufficiently regular map $f:\mathbb{T}\to {\mathbb{S}}^1$ is given in terms of its Fourier coefficients by $$ \operatorname{deg} f = \sum_{n\in\…