Infinite Order Differential Operators in Spaces of Entire Functions

Boundary value problem for an infinite system of second order differential equations in $\ell_p$ spaces

In this paper the concept of measure of noncompactness is applied to prove the existence of solution for a boundary value problem for an infinite system of second order differential equations in $\ell_{p}$ space. We change the boundary value problem into an equivalent system of infinite integral equations and obtain the result for the system of integral equations, using Darbo type fixed point theorem. The result is applied to an example to illustrate the concept.

给定近似阶的整单演函数与连续同态

Entire monogenic functions of given proximate order and continuous homomorphisms

本文受量子力学中无限阶微分算子启发，引入近似阶研究整单演函数空间上的同态，刻画了其上连续作用的无限阶微分算子，为相关算子理论提供了新结果。

全纯切片单演函数上连续同态的刻画

Characterization of continuous homomorphisms on entire slice monogenic functions

本文研究切片超全纯函数空间上无穷阶微分算子的连续作用，通过引入 proximate order 概念并建立相关基本性质，实现了对这类算子的刻画。

Monotone iterative schemes for positive solutions of a fractional differential system with integral boundary conditions on an infinite interval

In this paper, using the monotone iterative technique and the Banach contraction mapping principle, we study a class of fractional differential system with integral boundary on an infinite interval. Some explicit monotone iterative schemes for approximating the extreme positive solutions and the unique positive solution are constructed.

On higher index differential-algebraic equations in infinite dimensions

We consider initial value problems for differential-algebraic equations in a possibly infinite-dimensional Hilbert space. Assuming a growth condition for the associated operator pencil, we prove existence and uniqueness of solutions for arbitrary initial values in a distributional sense. Moreover, we construct a nested sequence of subspaces for initial values in order to obtain classical solutions.

论无穷维微分代数方程的魏尔斯特拉斯（Weierstraß）形式

On the Weierstraß form of infinite dimensional differential algebraic equations

本文研究带预解指数和魏尔斯特拉斯形式的无穷维微分代数方程的可解性，利用积分半群确定解存在唯一的子集，并将结果应用于端口哈密顿微分代数方程系统。

On Differential-Algebraic Equations in Infinite Dimensions

We consider a class of differential-algebraic equations (DAEs) with index zero in an infinite dimensional Hilbert space. We define a space of consistent initial values, which lead to classical continuously differential solutions for the associated DAE. Moreover, we show that for arbitrary initial values we obtain mild solutions for the associated problem. We discuss the asymptotic behaviour of solutions for both problems. In particular, we provide a characterisation for exponential stability and exponential dichotomies in terms of the spectrum of the associated operator pencil.

Aspects of differential calculus related to infinite-dimensional vector bundles and Poisson vector spaces

We prove various results in infinite-dimensional differential calculus which relate differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: 1. in the theory of infinite-dimensional vector bundles, to construct new bundles from given ones, like dual bundles, topological tensor products, infinite direct sums, and completions (under suitable hypotheses). 2. in the theory of locally convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity of passage from a function to the associat…

通过非紧性测度的算子型凝聚映射的最佳邻近点结果及其在$c_0$和$\boldsymbol{\textit{l}}_1$中无穷微分方程组的应用

Best proximity point results of operator type condensing mappings via measure of noncompactness and application to an infinite system of differential equations in $c_0$ and $\ell_1$

该研究提出新型算子型凝聚映射，借助非紧性测度建立最佳邻近点存在条件，并将其应用于求解$c_0$和$\boldsymbol{\textit{l}}_1$中的无穷微分方程组最优解。

Hypercyclicity of convolution operators on spaces of entire functions

In this paper we use Nachbin's holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables.

Spectral asymptotics for infinite order pseudo-differential operators

We study spectral properties of a class of global infinite order pseudo-differential operators and obtain the asymptotic behaviour of the spectral counting functions of such operators. Unlike their finite order counterparts, their spectral asymptotics are not of power-log-type but of log-type. The ultradistributional setting of such operators of infinite order makes the theory more complex so that the standard finite order global Weyl calculus cannot be used in this context.

非线性偏微分方程的无穷维矩-SOS层级

Infinite-dimensional moment-SOS hierarchy for nonlinear partial differential equations

本文提出将一类非线性演化偏微分方程转化为无穷维空间上正测度矩的线性优化问题，并利用平方和表示构造可收敛的有限维半定松弛层级，通过热方程非线性扰动数值实验验证了方法的有效性。

非线性无穷维退化随机微分方程的亚耗散性

Hypocoercivity for non-linear infinite-dimensional degenerate stochastic differential equations

本文研究非线性无穷维退化随机微分方程，用预解式方法构造无穷维Langevin动力学弱解，结合亚耗散性方法与算子本质m-耗散性结果，证明L²指数遍历性，并应用于显式退化扩散方程。

Applications of hypocontinuous bilinear maps in infinite-dimensional differential calculus

Paradigms of bilinear maps f between locally convex spaces (like evaluation or composition) are not continuous, but merely hypocontinuous. We describe situations where, nonetheless, compositions of f with Keller C^n_c-maps (on suitable domains) are C^n_c. Our main applications concern holomorphic families of operators, and the foundations of locally convex Poisson vector spaces.