James F. Tian

collaborators

32 papers

math.CV2026

A finite-Point Schwarz-Pick Inequality

James Tian

We prove a finite-point version of the Schwarz-Pick inequality for holomorphic self-maps of the disk. The estimate compares Bergman Gram matrices built from several points and thei…

math.PR2026

Tree Coordinates and Range Martingales for Positive Operator-Valued Measures

James Tian

Positive operator-valued measures on a tree admit intrinsic local coordinates coming from the way each cylinder value splits into its children. We show that these local splittings,…

math.FA2026

Compression Covariance and Tangent kernels

James Tian

Let $A \geq 0$ be self-adjoint on a Hilbert space $H$ , let $T_{t} = e^{- t A}$ , and let $P$ be an orthogonal projection. Relative to the decomposition $H = P H \oplus P^{⊥} H$ , write \[ T…

math.FA2026

Ordered POVMs and Residual Collapse

James Tian

Ordered realizations of discrete POVMs are studied through a residual transform generated by sequential tests. One application of the transform replaces each coordinate by the effe…

math.FA2026

Wavelet-Packet Content for Positive Operators

Myung-Sin Song, James Tian

We study positive operator decompositions associated with rooted trees of orthogonal projections. In this sense, the refinement tree induces an ``MRA in $B (H)_{+}$ ''. To…

quant-ph2026

Graph Structured Operator Inequalities and Tsirelson-Type Bounds

James Tian

We establish operator norm bounds for bipartite tensor sums of self-adjoint contractions. The inequalities generalize the analytic structure underlying the Tsirelson and CHSH bound…