Sorin G. Gal, Constantin P. Niculescu
In this paper we extend Korovkin's theorem to the context of sequences of weakly nonlinear and monotone operators defined on certain Banach function spaces. Several examples illustrating the theory are included.
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In this paper we prove Korovkin type theorems for sequences of sublinear, monotone and weak additive operators acting on function spaces C(X); where X is a compact or a locally compact metric space. Our results are illustrated by a series of examples
In this paper we prove analogues of Korovkin's theorem in the context of weakly nonlinear and monotone operators acting on Banach lattices of functions of several variables. Our results concern the convergence almost everywhere, the convergence in measure and the convergence in $L^{p}$-norm. Several results illustrating the theory are also included.
Quantitative estimates of convergence in nonlinear operator extensions of Korovkin's theorems
该研究针对实连续函数空间上的弱非线性单调算子序列，给出Korovkin定理非线性版本收敛性的连续模量化定量估计，并附示例阐释理论。
On Korovkin-type theorems including exponential test functions on infinite intervals through power series convergence
本文针对经典收敛失效的情况，利用幂级数收敛性及积分可和性，建立了保留指数函数的Korovkin型逼近定理，并通过连续模分析了收敛速度。
Korovkin-type approximation for non-positive operators
本文发展几何方法，针对$C(X)$与$L^1[0,1]$上的一致有界算子序列证明Korovkin型定理，将其推广到$L^1(\boldsymbol{R})$情形，以非正的Grünwald插值算子为例验证该定理并给出数值示例。
Our main aim is to investigate the approximation properties for the summation integral type operators in a statistical sense. In this regard, we prove the statistical convergence theorem using well known Korovkin theorem and the degree of approximation is determined. Also using weight function, the weighted statistical convergence theorem with the help of Korovkin theorem is obtained. The statistical rate of convergence in the terms of modulus of continuity and function belonging to the Lipschitz class is obtained. To support the convergence results of the proposed operators to the function, g…
Rigidity of operator systems: tight extensions and noncommutative measurable structures
针对Arveson猜想反例，利用Pedersen非交换可测结构思想，证明不可约表示均为边界表示等价于所有表示有唯一紧致完全正扩张，并推广Korovkin--Saskin原理。
In a real Hilbert spaces H a smooth operator F is studied, whose derivative at each point of its domain is a symmetric operator. In terms of abstract boundary conditions locally self-adjoint extensions of this operator are described. We use some concepts and facts from symplectic differential geometry.
We extend the functional analytic approach to Colombeau-type spaces of nonlinear generalized functions in order to study algebras of tempered generalized functions. We obtain a definition of Fourier transform of nonlinear generalized functions which has a strict inversion theorem, agrees with the classical Fourier transform for tempered distributions and preserves well-known classical properties.
The problem involving the extension of functions from a certain class and defined on subdomains of the ambient space to the whole space is an old and a well investigated theme in analysis. A related question whether the extensions that result in the process may be chosen in a linear or a continuous manner between appropriate spaces of functions turns out to be highly nontrivial. That this holds for the class of continuous functions defined on metric spaces is the well-known Borsuk-Dugundji theorem which asserts that given a metric space M and a subspace S of M, each continuous function g on S …
The paper computes the spaces of extensions for the Schatten classes when they are regarded in its natural module structure over the algebra of bounded operators on the ground Hilbert space.
Monotone extensions into compact target sets in dual systems
本文在对偶系统的一般框架下，不假设分离性，研究单调扩展问题，建立了紧目标集公式，利用非线性和凸分析工具给出了存在性结果及充要条件，并应用于变分不等式。
Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear differential equations on a half-axis. In addition, we extend the methods and present new similar results for integral equations and Volterra-Stieltjes integral equations, a framework whose benefits include the unification of second order difference and differential equations. In so doing, we enlarge the class of nonlinearities and in some cases remove the distinction …
We consider a global, nonlinear version of the Whitney extension problem for manifold-valued smooth functions on closed domains $C$, with non-smooth boundary, in possibly non-compact manifolds. Assuming $C$ is a submanifold with corners, or is compact and locally convex with rough boundary, we prove that the restriction map from everywhere-defined functions is a submersion of locally convex manifolds and so admits local linear splittings on charts. This is achieved by considering the corresponding restriction map for locally convex spaces of compactly-supported sections of vector bundles, allo…
Given a linear semi-bounded symmetric operator $S\ge -ω$, we explicitly define, and provide their nonlinear resolvents, nonlinear maximal monotone operators $A_Θ$ of type $λ>ω$ (i.e. generators of one-parameter continuous nonlinear semi-groups of contractions of type $λ$) which coincide with the Friedrichs extension of $S$ on a convex set containing ${\mathscr D}(S)$. The extension parameter $Θ\subset{\mathfrak h}\times{\mathfrak h}$ ranges over the set of nonlinear maximal monotone relations on an auxiliary Hilbert space $\mathfrak h$ isomorphic to the deficiency subspace of $S$. Moreover $A_…
Some nonlinear extensions of the vector maximality statement established by Goepfert, Tammer and Zalinescu [Nonl. Anal., 39 (2000), 909-922] are given. Basic instruments for these are the Brezis-Browder ordering principle [Advances Math., 21 (1976), 355-364] and a (pseudometric) version of it obtained in Turinici [Demonstr. Math., 22 (1989), 213-228].
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