Logarithmic Trace of Toeplitz Projectors

Equivariant asymptotics for Toeplitz operators

In recent years, the Tian-Zelditch asymptotic expansion for the equivariant components of the Szegö kernel of a polarized complex projective manifold, and its subsequent generalizations in terms of scaling limits, have played an important role in algebraic, symplectic, and differential geometry. A natural question is whether there exist generalizations in which the projector onto the spaces of holomorphic sections can be replaced by the projector onto more general (non-complete) linear series. One case that lends itself to such analysis, and which is natural from the point of view of geometric…

Toeplitz determinants of Logarithmic coefficients for Starlike and Convex functions

In this study, we deal with the sharp bounds of certain Toeplitz determinants whose entries are the logarithmic coefficients of analytic univalent functions $f$ such that the quantity $z f'(z)/f(z)$ takes values in a specific domain lying in the right half plane. The established results provide the bounds for the classes of starlike and convex functions, as well as various of their subclasses.

关于类\\(\mathcal{S}_{car}^*\\)涉及对数系数与逆对数系数的Sharp Hankel行列式及Hermitian–Toeplitz行列式

Sharp Hankel and Hermitian--Toeplitz Determinants Involving Logarithmic and Inverse Logarithmic Coefficients for the class \(\mathcal{S}_{car}^*\)

本文针对与心脏线区域相关的星型函数类，推导了二阶对数系数与逆对数系数的Hankel行列式的sharp界，完整解决了三阶Hermitian–Toeplitz行列式的sharp极值问题，相关结果由极值实例验证。

与 Ma-Minda 类相关的反函数 Toeplitz 行列式及其对数系数

Toeplitz Determinants for Inverse Functions and their Logarithmic Coefficients Associated with Ma-Minda Classes

本文研究 Ma-Minda 型星形与凸函数类中反函数的系数及对数系数，给出相关 Toeplitz 行列式的精确界，并统一推广到多个已知子类。

关于某类单叶函数的逆函数对数系数的 Hankel 和 Toeplitz 行列式

Hankel and Toeplitz determinants of logarithmic coefficients of Inverse functions for certain classes of univalent functions

本文针对关于对称点的星形和凸函数类，建立了其逆函数对数系数的 Hankel 和 Toeplitz 行列式的精确不等式，并通过示例验证了结论。

The Cauchy problem for the homogeneous Monge-Ampere equation, I. Toeplitz quantization

The Cauchy problem for the homogeneous (real and complex) Monge-Ampere equation (HRMA/HCMA) arises from the initial value problem for geodesics in the space of Kahler metrics. It is an ill-posed problem. We conjecture that, in its lifespan, the solution can be obtained by Toeplitz quantizing the Hamiltonian flow defined by the Cauchy data, analytically continuing the quantization, and then taking a kind of logarithmic classical limit. In this article, we prove that in the case of torus invariant metrics (where the HCMA reduces to the HRMA) this "quantum analytic continuation potential" coincid…