A Monotone Selection Principle in C*-algebras

关于最大单调算子的入门笔记

A Beginner-Friendly Note on Maximal Monotone Operators

本文为初学者提供了一个关于最大单调算子的入门概述，介绍了相关泛函分析工具及Brézis定理的核心内容。

Dynamical Systems Method for solving nonlinear equations with locally Holder continuous monotone operators

A version of the Dynamical Systems Method for solving ill-posed nonlinear equations with monotone and locally Hölder continuous operators is studied in this paper. A discrepancy principle is proposed and justified under natural and weak assumptions. The only smoothness assumption on $F$ is the local Hölder continuity of order $α>1/2$.

Sharp finiteness principles for Lipschitz selections: long version

Let $({\mathcal M},ρ)$ be a metric space and let $Y$ be a Banach space. Given a positive integer $m$, let $F$ be a set-valued mapping from ${\mathcal M}$ into the family of all compact convex subsets of $Y$ of dimension at most $m$. In this paper we prove a finiteness principle for the existence of a Lipschitz selection of $F$ with the sharp value of the finiteness number.

算子序列在压缩支配意义下的单调性

Sequences of operators, monotone in the sense of contractive domination

本文证明在压缩支配意义下非递减的算子序列具有线性算子极限，且可闭性或闭性在极限中保持，并探讨了闭包收敛及非递增序列的相关结果。

Sharp finiteness principles for Lipschitz selections

Let $(M,ρ)$ be a metric space and let $Y$ be a Banach space. Given a positive integer $m$, let $F$ be a set-valued mapping from $M$ into the family of all compact convex subsets of $Y$ of dimension at most $m$. In this paper we prove a finiteness principle for the existence of a Lipschitz selection of $F$ with the sharp value of the finiteness constant.

Existence of recombination-selection equilibria for sexual populations

We study a birth and death model for the adapatation of a sexual population to an environment. The population is structured by a phenotypical trait, and, possibly, an age variable. Recombination is modeled by Fisher's infinitesimal operator. We prove the existence of principal eigenelements for the corresponding eigenproblem. As the infinitesimal operator is 1-homogeneous but nor linear nor monotone, the general Krein-Rutman theory cannot be applied to this problem.

对偶空间严格凸的 Banach 空间中 (D) 型极大单调算子的表示公式

Representation formulas for maximal monotone operators of type (D) in Banach spaces whose dual spaces are strictly convex

针对对偶空间严格凸的 Banach 空间中的 (D) 型极大单调算子，通过邻近点值建立其值及支撑函数的表示公式。

Finiteness Principles for Smooth Selection

In this paper we prove finiteness principles for $C^{m}\left( \mathbb{R}^{n}, \mathbb{R}^{D}\right) $-selection, and for $C^{m-1,1}\left( \mathbb{R}^{n}, \mathbb{R}^{D}\right) $-selection, in particular providing a proof for a conjecture of Brudyni-Shvartsman (1994) on Lipschitz selections for the case when the domain is $X = \mathbb{R}^n$. Our results raise the hope that one can start to understand constrained interpolation problems in which e.g. the interpolating function $F$ is required to be nonnegative everywhere.

Finitness Principles for Smooth Selection

In this paper we prove finiteness principles for $C^{m}\left( \mathbb{R}^{n}, \mathbb{R}^{D}\right) $-selection, and for $C^{m-1,1}\left( \mathbb{R}^{n}, \mathbb{R}^{D}\right) $-selection, in particular providing a proof for a conjecture of Brudyni-Shvartsman (1994) on Lipschitz selections for the case when the domain is $X = \mathbb{R}^n$.