多齐努-弗罗本ius定理的多齐努-弗罗本ius映射

非负多重线性形式的Perron-Frobenius定理及其推广

Perron-Frobenius theorem for nonnegative multilinear forms and extensions

本文证明了非负系数多重线性形式（更一般地，非负系数多项式映射）的Perron-Frobenius定理，并确定了幂算法收敛到唯一归一化特征向量的几何收敛速度。

The Perron-Frobenius theorem for multi-homogeneous mappings

The Perron-Frobenius theory for nonnegative matrices has been generalized to order-preserving homogeneous mappings on a cone and more recently to nonnegative multilinear forms. We unify both approaches by introducing the concept of order-preserving multi-homogeneous mappings, their associated nonlinear spectral problems and spectral radii. We show several Perron-Frobenius type results for these mappings addressing existence, uniqueness and maximality of nonnegative and positive eigenpairs. We prove a Collatz-Wielandt principle and other characterizations of the spectral radius and analyze the …

非负张量的张量范数和最大奇异向量 - 一个广义的Perron-Frobenius定理，一个Collatz-Wielandt特征描述和一个广义幂方法

Tensor norm and maximal singular vectors of non-negative tensors - a Perron-Frobenius theorem, a Collatz-Wielandt characterization and a generalized power method

本文研究非负张量的l^{p1,...,pm}奇异值问题，提出广义幂方法并证明其渐近线性收敛性。

A unifying Perron-Frobenius theorem for nonnegative tensors via multi-homogeneous maps

We introduce the concept of shape partition of a tensor and formulate a general tensor eigenvalue problem that includes all previously studied eigenvalue problems as special cases. We formulate irreducibility and symmetry properties of a nonnegative tensor $T$ in terms of the associated shape partition. We recast the eigenvalue problem for $T$ as a fixed point problem on a suitable product of projective spaces. This allows us to use the theory of multi-homogeneous order-preserving maps to derive a new and unifying Perron-Frobenius theorem for nonnegative tensors which either implies earlier re…

Further Results for Perron-Frobenius Theorem for Nonnegative Tensors II

In this paper, we generalize some conclusions from the nonnegative irreducible tensor to the nonnegative weakly irreducible tensor and give more properties of eigenvalue problems.

Noncommutative Perron-Frobenius-Ruelle theorem, two weight Hilbert transform, and almost periodicity

We consider the Jacobi matrix generated by a balanced measure of hyperbolic polynomial map. The conjecture of Bellissard says that this matrix should have an extremely strong periodicity property. We show how this conjecture is related to a certain noncommutative version of Bowen--Ruelle theory, and how the two weight Hilbert transform naturally appears in this context.