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pro vyhledávání: '"47a05"'
In this paper, we introduce the generalized Cauchy dual $w(T) = T(T^{*}T)^{\dagger}$ of a closed operator $T$ with the closed range between Hilbert spaces and present intriguing findings that characterize the Cauchy dual of $T$. Additionally, we esta
Externí odkaz:
http://arxiv.org/abs/2412.12313
Autor:
Khachiaa, Najib
This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( \mathcal{H} \), where \( K \) is a right $\mathbb{H}$-linear bounded op
Externí odkaz:
http://arxiv.org/abs/2411.07937
Autor:
Khachiaa, Najib
The aim of this paper is to study $K$-frames for quaternionic Hilbert spaces. First, we present the quaternionic version of Douglas's theorem and then investigate $K$-frames for a quaternionic Hilbert space $\mathcal{H}$, where $K \in \mathbb{B}(\mat
Externí odkaz:
http://arxiv.org/abs/2411.04154
In this paper, we study an inverse problem of identifying two spatial-temporal source terms in the Schr\"odinger equation with dynamic boundary conditions from the final time overdetermination. We adopt a weak solution approach to solve the inverse s
Externí odkaz:
http://arxiv.org/abs/2410.21123
Autor:
Majumdar, Arup, Johnson, P. Sam
In this paper, we present intriguing findings that characterize both the closed (unbounded) and bounded EP operators on Hilbert spaces. Additionally, we demonstrate the result $\gamma(T) \leq r(T)$, where $T$ is a bounded EP operator, and $\gamma(T)
Externí odkaz:
http://arxiv.org/abs/2410.06869
Autor:
Laghmam, Btissam, Zguitti, Hassane
In this paper we introduce the notion of $(b,c)$-polar elements in an associative ring $R$. Necessary and sufficient conditions of an element $a\in R$ to be $(b,c)$-polar are investigated. We show that an element $a\in R$ is $(b,c)$-polar if and only
Externí odkaz:
http://arxiv.org/abs/2409.11987
This paper introduces and investigates the concept of the $q$-numerical range for tuples of bounded linear operators in Hilbert spaces. We establish various inequalities concerning the $q$-numerical radius associated with these operator tuples. Furth
Externí odkaz:
http://arxiv.org/abs/2410.03669
Autor:
Bhandari, Animesh
Fusion frames are widely studied for their applications in recovering signals from large data. These are proved to be very useful in many areas, such as, distributed processing, wireless sensor networks, packet encoding. Inspired by the work of Bemro
Externí odkaz:
http://arxiv.org/abs/2409.01288
Autor:
Wang, Yicao
Based on the relationship of symmetric operators with Hermitian symmetric spaces, we introduce the notion of \emph{Weyl curve} for a symmetric operator $T$, which is the geometric abstraction and generalization of the well-known Weyl functions. We pr
Externí odkaz:
http://arxiv.org/abs/2408.10968
Autor:
Restrepo, Joel E.
We show the explicit solution operator of an abstract Cauchy problem involving a time-variable coefficient and a fractional power of an almost sectorial operator. Also, by using the representation of the solution operator, we solve the inverse abstra
Externí odkaz:
http://arxiv.org/abs/2408.00240