Mikhail I. Ostrovskii
The condition onto pair ($F,G$) of function Banach spaces under which there exists a integral operator $T:F\to G$ with analytic kernel such that the inverse mapping $T^{-1}:$im$T\to F$ does not belong to arbitrary a priori given Borel (or Baire) class is found.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
This note aims to investigate the tensor product of two given Hilbert quasi *-algebras and its properties. The construction proposed in this note turns out to be again a Hilbert quasi *-algebra, thus interesting representability properties studed in \cite{AT} are maintained. Furthermore, if two functionals are representable and continuous respectively on the two Hilbert quasi *-algebras, then so is their tensor product.
We consider the problem of the representation of real continuous functions by linear superpositions $\sum_{i=1}^{k}g_{i}\circ p_{i}$ with continuous $g_{i}$ and $p_{i}$. This problem was considered by many authors. But complete, and at the same time explicit and practical solutions to the problem was given only for the case $k=2$. For $k>2$, a rather practical sufficient condition for the representation can be found in Sternfeld [17] and Sproston, Strauss [16]. In this short note, we give a necessary condition of such kind for the representability of continuous functions.
Special properties of Gossez's example
本文研究了 Gossez 例子在两个自然对偶系统中的可表示性、闭性与极大单调性，并给出了相关的新性质。
A note concerning fundamental functions of interpolation associated to the inverse multiquadric $(α^2+x^2)^{-k}$
本文针对逆多重二次函数 $(α^2+x^2)^{-k}$ 的散乱平移，构造并研究了相应的基本插值函数。
We prove the theorem converse to Jackson's theorem for a modulus of smoothness of the first order generalised by means of an asymmetric operator of generalised translation.
In this paper presents the results obtained in the field of spectral theory operators of fractional differentiation. Proven a number of propositions which represents independent interest in the theory of fractional calculus. Introduced construction of multidimensional fractional integral in the direction. Formulated the sufficient conditions of representability functions by the fractional integral in the direction, in particular proved the embedding of a Sobolev space in classes of functions representable by the fractional integral in direction. Note that the technique of proof borrowed from t…
The aim of this note is to study existence and main properties of direct and inverse limits in the category of normed $L^0$-modules (in the sense of Gigli) over a metric measure space.
Please, not \textit{another} note about Generalized Inverses
该研究针对非递减实函数的广义逆问题，证明了其左连续与右连续变体的相关结论，补充了广义逆理论的相关结果。
A note on Boolean inverse monoids and ample groupoids
本文研究布尔逆幺半群与 ample 群胚之间的联系，通过具体构造和性质分析，揭示了二者之间的对应关系。
In this note, we provide some sufficient and necessary conditions for the core inverse of the perturbed operator to have the simplest possible expression. The results improve the recent work by H. Ma (Optimal perturbation bounds for the core inverse, Appl. Math. Comput. 336 (2018) 176-181.).
A note on the Krylov solvability of compact normal operators on Hilbert space
本文研究 Hilbert 空间上紧正规算子逆线性问题的 Krylov 可解性，显式刻画其 Krylov 子空间，证明值域内数据对应问题均可解，并建立闭 Krylov 子空间与 $L^2$-测度空间的同构。
Hadamard's global inverse theorem provides conditions for a function to be globally invertible on Rn. In this note we show that the conditions are robust enough for the conclusion to hold even if we relax the conditions by removing the assumption at a finite number of points. As a consequence, we get a global inverse function theorem for homogeneous functions.
The main concern of this note is the Moore-Penrose inverse in the context of Banach spaces and algebras. Especially attention will be given to a particular class of elements with the aforementioned inverse, namely EP Banach space operators and Banach algebra elements, which will be studied and characterized extending well-known results obtained in the frame of Hilbert space operators and $C^*$-algebra elements.
A note on the positivity of inverse operators acting on $C^*$-algebras
本文研究 $C^*$-代数上正可逆线性算子的逆算子正性问题，给出了 $T^{-1}$ 为正的充要条件，并通过反例说明即使 $T$ 为单位算子且谱在单位圆内，其逆算子也未必为正。
Let $K,\,H$ be Hilbert spaces and let $L(K,H)$ denote the set of all bounded linear operators from $K$ to $H$. Let $A \in L(H)\triangleq L(H,H)$ with $R(A)$ closed and $X,Y \in L(K,H)$ with $R(X)\subseteq R(A),R(Y)\subseteq R(A^*)$. In this short note, we give some new expressions of the Moore--Penrose inverse $(A-XY^*)^+$ of $A-XY^*$ under certain suitable conditions.
We consider variational regularization of nonlinear inverse problems in Banach spaces using Tikhonov functionals. This article addresses the problem of $Γ$-convergence of a family of Tikhonov functionals and assertions of the convergence of their respective infima. Such questions arise, if model uncertainties, inaccurate forward operators, finite dimensional approximations of the forward solutions and / or data, etc. make the evaluation of the original functional impossible and, thus, its minimizer not computable. But for applications it is of utmost importance that the minimizer of the replac…
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral filters as well as the concrete examples of Tikhonov regularization, Landweber iteration, regularization by discretization for linear inverse problems. In the nonlinear setting, Tikhonov regularization and iterative regularization (Landweber, Levenberg-Marquardt, and iteratively regularized Gauß-Newton methods) are discussed. The necessary background from fu…
The Schur algebra is the algebra of operators which are bounded on l^1 and on l^{\infty}. Q. Sun conjectured that the Schur algebra is inverse-closed. In this note, we disprove this conjecture. Precisely, we exhibit an operator in the Schur algebra, invertible in l^2, whose inverse is not bounded on l^1 nor on l^{\infty}.
In this paper, we introduce the m-core-EP inverse in Minkowski space, consider its properties, and get several sufficient and necessary conditions for the existence of the m-core-EP inverse. We give the m-core-EP decomposition in Minkowski space, and note that not every square matrix has the decomposition. Furthermore, by applying the m-core-EP inverse and the m-core-EP decomposition, we introduce the m-core-EP order and give some characterizations of it.
Banach algebra crossed products by inverse semigroup actions
本文提出了一种对逆半群作用下的巴拿赫代数交叉积进行普遍描述的方法，允许对交叉积的所有表示进行分解。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。