22 papers
The Hayman--Wu constant is
Paata Ivanisvili
We show that for every conformal map from the unit disk onto a simply connected proper domain , the length of is at most…
A counterexample to the Kato conjecture for positive commutators
Rupert L. Frank, Paata Ivanisvili
We disprove the conjectural converse to Kato's positivity criterion for commutators of functions of the canonical position and momentum operators and by showing that the op…
Counterexamples to the Landis conjecture in dimensions three and higher
Rupert L. Frank, Paata Ivanisvili
In every dimension three and higher we construct a nonzero function that satisfies the stationary Schrödinger equation with bounded, real-valued potential and decays like $\exp(-c…
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 is given in terms of its Fourier coefficients by $$ \operatorname{deg} f = \sum_{n\in\…
The missing two-point inequality in Weissler's conjecture
Yi C. Huang, Paata Ivanisvili
Weissler's conjectured characterization of complex hypercontractivity on the Hamming cube remained open in the ranges and . Ivanisvili--Nazarov estab…
A Beckmann boundary form of Talagrand's conjecture on the discrete cube
Paata Ivanisvili, Xinyuan Xie, Haonan Zhang
We introduce the Beckmann boundary of a Boolean function \[ \mathsf{B}(f)=\inf_{\operatorname{div} V=Lf}\mathbb E\|V(x)\|_2. \] Here \[ L=\sum_iD_i,\qquad D_i f(x)=\frac{f(x)-f(x^{…