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Carleson measures and the boundedness of singular integral operators on Q-type spaces related to weights
Springer Science and Business Media LLC - Tập 13 - Trang 1-32 - 2021
Xuan Chen, Pengtao Li, Zengjian Lou
In this paper, by the aid of the Poisson integral, we establish a Carleson type characterization of Q type spaces $$Q^{p}_{{\mathcal {K}}}({\mathbb {R}}^{n})$$ $$(n\ge 1)$$ with weight K. As an ap...... hiện toàn bộ
On creating new essential spectrum by self-adjoint extension of gapped operators
Springer Science and Business Media LLC - Tập 15 - Trang 1-24 - 2024
Alessandro Michelangeli
Given a densely defined and gapped symmetric operator with infinite deficiency index, it is shown how self-adjoint extensions admitting arbitrarily prescribed portions of the gap as essential spectrum are identified and constructed within a general extension scheme. The emergence of new spectrum in the gap by self-adjoint extension is a problem with a long history and recent deep understanding, an...... hiện toàn bộ
Ultraholomorphic sectorial extensions of Beurling type
Springer Science and Business Media LLC - Tập 12 - Trang 1-20 - 2021
David Nicolas Nenning, Armin Rainer, Gerhard Schindl
We prove sectorial extension theorems for ultraholomorphic function classes of Beurling type defined by weight functions with a controlled loss of regularity. The proofs are based on a reduction lemma, due to the second author, which allows to extract the Beurling from the Roumieu case, which was treated recently by Jiménez-Garrido, Sanz, and the third author. To have control on the opening of the...... hiện toàn bộ
Complexity of Monte Carlo integration for Besov classes on the unit sphere
Springer Science and Business Media LLC - Tập 14 - Trang 1-18 - 2022
Liqin Duan, Peixin Ye, Wan Li
We obtain the exact orders of the complexity of the integration of functions from Besov classes $$BB_{p,\theta }^\Omega$$ on the unit sphere of d-dimensional Euclidean space in the deterministic and randomized settings. The corresponding optimal quadrature rules have been constructed in both setti...... hiện toàn bộ
The Weyl–von Neumann theorem for skew-symmetric operators
Springer Science and Business Media LLC - Tập 14 - Trang 1-12 - 2023
Qinggang Bu, Sen Zhu
We consider the diagonalization of self-adjoint operators in the infinite-dimensional orthogonal Lie algebra $$\mathcal O_C$$ , which consists of all bounded linear operators T on a separable, infinite-dimensional, complex Hilbert space ...... hiện toàn bộ
The extension problem in free harmonic analysis
Springer Science and Business Media LLC - Tập 13 - Trang 1-27 - 2022
Peter Burton, Kate Juschenko
This paper studies certain aspects of harmonic analysis on nonabelian free groups. We focus on the concept of a positive definite function on the free group and our primary goal is to understand how such functions can be extended from balls of finite radius to the entire group. Previous work showed that such extensions always exist and we study the problem of simultaneous extension of multiple pos...... hiện toàn bộ
Properties of two unitary operator functions involving idempotents
Springer Science and Business Media LLC - Tập 11 - Trang 540-554 - 2019
Jiaxin Zhang, Jiajia Niu, Yuan Li
Let P be an idempotent operator on a Hilbert space $$\mathcal {H}.$$ We denote two unitary operator functions $$U_{\lambda }$$ and $$V_{\lambda }$$ by $$\begin{aligned} U_{\lambda }:=(\lambda P+I)|\lambda P+I|^{-1} \hbox { } \hbox { and }\hbox { } V_{\lambda }:=(\lambda P^{*}+I)|\lambda P^{*}+I|^{-1}, \ \ \hbox { for }\lambda \in \mathbb {C}\backslash \{-1\}. \end{aligned}$$ In this pap...... hiện toàn bộ
On normed spaces with the Wigner Property
Springer Science and Business Media LLC - Tập 11 - Trang 523-539 - 2019
Ruidong Wang, Dariusz Bugajewski
The aim of this paper is to generalize the Wigner Theorem to real normed spaces. A normed space is said to have the Wigner Property if the Wigner Theorem holds for it. We prove that every two-dimensional real normed space has the Wigner Property. We also study the Wigner Property of real normed spaces of dimension at least three. It is also shown that strictly convex real normed spaces possess the...... hiện toàn bộ
System of generalized nonlinear variational-like inequalities and nearly asymptotically nonexpansive mappings: graph convergence and fixed point problems
Springer Science and Business Media LLC - Tập 13 - Trang 1-44 - 2022
Javad Balooee, Mihai Postolache, Yonghong Yao
In this paper, with the goal of investigating the problem of finding a common element of the set of fixed points of a nearly asymptotically nonexpansive mapping and the set of solutions of a system of generalized nonlinear variational-like inequalities, an iterative algorithm is proposed. The notions of graph convergence and P– $...... hiện toàn bộ
The generalized Fredholm elements in a semisimple Banach algebra
Springer Science and Business Media LLC - - 2022
Yingying Kong, Lining Jiang, Yanxun Ren
Tổng số: 226   
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