Vitali-type theorems for filter convergence related to vector lattice-valued modulars and applications to stochastic processes

向量值模形式的标准 $L$-函数

The standard $L$-function attached to a vector valued modular form

本文为向量值模形式定义了两个相关的 $L$-函数（一个基于特征值的 zeta 函数，一个基于欧拉乘积），并证明它们可亚纯延拓至整个复平面。

Weakly stationary stochastic processes valued in a separable Hilbert space: Gramian-Cramér representations and applications

The spectral theory for weakly stationary processes valued in a separable Hilbert space has known renewed interest in the past decade. Here we follow earlier approaches which fully exploit the normal Hilbert module property of the time domain. The key point is to build the Gramian-Cramér representation as an isomorphic mapping from the modular spectral domain to the modular time domain. We also discuss the general Bochner theorem and provide useful results on the composition and inversion of lag-invariant linear filters. Finally, we derive the Cramér-Karhunen-Loève decomposition and harmonic f…

算子值扭曲Araki-Woods代数

Operator-Valued Twisted Araki-Woods Algebras

本文引入算子值扭曲Araki-Woods代数，发展将其归结为标量值情形的解体理论，刻画其自然权重的模理论，并给出保证代数因子性的充分判据。

Rates of convergence for iterative solutions of equations involving set-valued accretive operators

This paper studies proofs of strong convergence of various iterative algorithms for computing the unique zeros of set-valued accretive operators that also satisfy some weak form of uniform accretivity at zero. More precisely, we extract explicit rates of convergence from these proofs which depend on a modulus of uniform accretivity at zero, a concept first introduced by A. Koutsoukou-Argyraki and the first author in 2015. Our highly modular approach, which is inspired by the logic-based proof mining paradigm, also establishes that a number of seemingly unrelated convergence proofs in the liter…