10 papers
Beurling--Carleson Endpoint Counterexamples: Singular Inner Functions and a Semilinear Equation
Pengcheng Fang, Yixin He
We settle two endpoint problems for Beurling--Carleson support conditions. For and , we construct a nonatomic singular probability measure , su…
Variable-Radius Disk Transforms and an Area-Integral Problem of Zalcman
Qiteng Guo, Yixin He
For , define for , where is planar Lebesgue measure. We prove that is injective…
A proof of the Ashbaugh--Benguria conjecture for reciprocal sums of Neumann eigenvalues
Yixin He, Yanyang Li, Quanyu Tang
We prove the Ashbaugh--Benguria conjecture for bounded domains with smooth boundary in . More precisely, among all smooth bounded domains of fixed volume, the ball min…
The separable case of Kadison's problem on orthonormal bases of unitaries for type factors
Yixin He, Quanyu Tang, Teng Zhang
In 1967, Kadison asked ``does every type factor have an orthonormal (with respect to the trace) basis consisting of unitaries?'' Using a noncommutative Lyapunov the…
Optimal universal growth for integral means of normalized logarithmic derivatives in the Carathéodory class
Yixin He, Quanyu Tang, Teng Zhang
We determine the optimal universal growth scale for the integral means of normalized logarithmic derivatives in the Carathéodory class. This resolves a problem of D.~K.~Thomas.
A Solution to a Problem of Rubel on Two-Parameter Normal Families of Entire Functions
Yixin He, Quanyu Tang, Teng Zhang
We construct an entire function such that the family of entire functions of \(z\) is normal on…