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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
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 application, we prove that convolution
singular integral operators are bounded on $$Q^{p}_{{\mathcal {K}}}({\mathbb
{R}}^{n})$$ for $$n\ge 2$$ ....
On creating new essential spectrum by self-adjoint extension of gapped operators
Springer Science and Business Media LLC - Tập 15 - Trang 1-24 - 2024
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...
Ultraholomorphic sectorial extensions of Beurling type
Springer Science and Business Media LLC - Tập 12 - Trang 1-20 - 2021
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...
Complexity of Monte Carlo integration for Besov classes on the unit sphere
Springer Science and Business Media LLC - Tập 14 - Trang 1-18 - 2022
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 settings. Our results
show that Monte Carlo algorithm can provide a faster convergence rate than that
of th...
The Weyl–von Neumann theorem for skew-symmetric operators
Springer Science and Business Media LLC - Tập 14 - Trang 1-12 - 2023
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 $$\mathcal {H}$$ satisfying $$CTC = -T^*$$ , where C is a
conjugation on $$\mathcal H$$ . First, we establish the Weyl–von Neumann Theorem
in $$\mathcal {O}_C$$ , ...
The extension problem in free harmonic analysis
Springer Science and Business Media LLC - Tập 13 - Trang 1-27 - 2022
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...
Properties of two unitary operator functions involving idempotents
Springer Science and Business Media LLC - Tập 11 - Trang 540-554 - 2019
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
paper, we firs...
On normed spaces with the Wigner Property
Springer Science and Business Media LLC - Tập 11 - Trang 523-539 - 2019
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...
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
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– $$\eta$$ -proximal point mapping are used and a new
equivalence relati...
The generalized Fredholm elements in a semisimple Banach algebra
Springer Science and Business Media LLC - - 2022
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