An Operator Theorem on $L_1$ Convergence to Zero with Applications to Markov Kernels

An Artin-rees Theorem and Applications to Zero Cycles

For the smooth normalization f : X → X of a singular variety X over a field k of characteristic zero, we show that for any conducting subscheme Y for the normalization, and for any i ∈ Z, the natural map Ki(X, X, nY ) → Ki(X, X, Y ) is zero for all sufficiently large n. As an application, we prove a formula for the Chow group of zero cycles on a quasi-projective variety X over k with Cohen-Maca...

Nonlinear Picone identities to Pseudo $p$-Laplace operator and applications

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

An Infinite Dimensional Schur-horn Theorem and Majorization Theory with Applications to Operator Ideals

The main result of this paper is the extension of the Schur-Horn Theorem to infinite sequences: For two nonincreasing nonsummable sequences ξ and η that converge to 0, there exists a positive compact operator A with eigenvalue list η and diagonal sequence ξ if and only if Pn j=1 ξj ≤ Pn j=1 ηj for every n if and only if ξ = Qη for some orthostochastic matrix Q. When ξ and η are summable, requir...

A class of $L_1$-to-$L_1$ and $L_\infty$-to-$L_\infty$ interval observers for (delayed) Markov jump linear systems

We exploit recent results on the stability and performance analysis of positive Markov jump linear systems (MJLS) for the design of interval observers for MJLS with and without delays. While the conditions for the L1 performance are necessary and sufficient, those for the L∞ performance are only sufficient. All the conditions are stated as linear programs that can be solved very efficiently. Tw...

An unbounded Berge's minimum theorem with applications to discounted Markov decision processes