Uniqueness theorems for (sub-)harmonic functions with applications to operator theory

Boundary uniqueness of harmonic functions and spectral subspaces of operator groups

We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on Banach spaces.

Uniqueness property for quasiharmonic functions

In this paper we consider class of continuous functions, called quasiaharmonic functions, admitting best approximations by harmonic polynomials. In this class we prove a uniqueness theorem by analogy with the analytic functions.

Uniqueness theorems for subharmonic functions

It is shown that harmonic functions on some subsets, subharmonic and coinciding everywhere outside of these sets, actually coincide everywhere.

三次球定理对于调和函数（非同心情况)

Three-spheres theorem for harmonic functions (non-concentric case)

研究非同心球体中调和函数的三次球定理，通过倒置技术扩展到相关非同心非接触球体，并应用于小量传播和调和函数的唯一性。

A generalization of trigonometric convexity and its relation to positive harmonic functions in homogeneous domains

We consider functions which are subfunctions with respect to the differential operator $$L_ρ= \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + 2ρ\frac{\partial}{\partial x} + ρ^2 $$ and are doubly periodic in the plane. These functions play an important role in describing the asymptotic behavior of entire and subharmonic functions of finite order. In studying their properties we are led to problems concerning the uniqueness of Martin functions and the critical value for the parameter $ρ$ in the homogeneous boundary problem for the operator $L_ρ$ in a domain on the torus.

调和分析中的不确定性原理——精选主题讲义

The Uncertainty Principle in Harmonic Analysis -- Lecture Notes on Selected Topics

本文通过 Fourier 级数与变换的唯一性和重建问题、频谱间隙影响及对数可积性在逼近与拟解析性中的作用，探讨了不确定性原理的多个经典表现，涵盖 Paley-Wiener 定理等核心结果。