相关论文: Landweber-type operator and its properties

We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems…

Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…

Linear differential equations with variable coefficients and Prabhakar-type operators featuring Mittag-Leffler kernels are solved. In each case, the unique solution is constructed explicitly as a convergent infinite series involving…

The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant…

Operator splitting techniques have recently gained popularity in convex optimization problems arising in various control fields. Being fixed-point iterations of nonexpansive operators, such methods suffer many well known downsides, which…

In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…

We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the…

The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schr\"{o}dinger equations. However, when applied to certain nonlinear time-dependent Schr\"{o}dinger equations, this algorithm loses…

We study variational inequalities which are governed by a strongly monotone and Lipschitz continuous operator $F$ over a closed and convex set $S$. We assume that $S=C\cap A^{-1}(Q)$ is the nonempty solution set of a (multiple-set) split…

We study some basic properties of the class of universal operators on Hilbert space, and provide new examples of universal operators and universal pairs.

Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous…

This paper considers computational methods that split a vector field into three components in the case when both the vector field and the split components might be unbounded. We first employ classical Taylor expansion which, after some…

This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…

We introduce Wirtinger operators for functions of several quaternionic variables. These operators are real linear partial differential operators which behave well on quaternionic polynomials, with properties analogous to the ones satisfied…

A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration…

Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…

The purpose of this paper is concerned with the approximate solution of split equality problems. We introduce two types of algorithms and a new self-adaptive stepsize without prior knowledge of operator norms. The corresponding strong…

In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…

We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…

A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite…