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Resolvent Positive Operators and Positive Fractional Resolvent Families [PDF]
Journal of Function Spaces, 2021 This paper is concerned with positive α-times resolvent families on an ordered Banach space E (with normal and generating cone), where ...
Nan-Ding Li, Ru Liu, Miao Li
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Spectrum of a family of operators [PDF]
Surveys in Mathematics and its Applications, 2011 Having as start point the classic definitions of resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the resolvent set and spectrum of a family of linear bounded operators on a Banach space.
Simona Macovei
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Fractional resolvent family generated by normal operators
AIMS Mathematics, 2023 The main focus of this paper is on the relationship between the spectrum of generators and the regularity of the fractional resolvent family. We will give a counter-example to show that the point-spectral mapping theorem is not valid for $ \{S_{\alpha}(t)
Chen-Yu Li
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Strong coupling limit of a family of Chern-Simons-matter theories
Journal of High Energy Physics, 2018 We investigate the strong coupling limit of a family of Chern-Simons-matter theories in the planar limit. The family consists of N=3 $$ \mathcal{N}=3 $$ theories with the gauge group UN1k1×UN2k2 $$ \mathrm{U}{\left({N}_1\right)}_{k_1} \times \mathrm{U ...
Takao Suyama
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Representation and stability of distributed order resolvent families
AIMS Mathematics, 2022 We consider the resolvent family of the following abstract Cauchy problem (1.1) with distributed order Caputo derivative, where A is a closed operator with dense domain and satisfies some further conditions.
Chen-Yu Li
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Universal Journal of Mathematics and Applications, 2023 This work aims to study the existing results of mild solutions for a semi-linear Atangana-Baleanu-Caputo fractional differential equation with order $ 0 < \theta < 1 $ in an arbitrary Banach space.
Khalid Hilal +2 more
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Approximation of point interactions by geometric perturbations in two-dimensional domains
Bulletin of Mathematical Sciences, 2023 In this paper, we present a new type of approximation of a second-order elliptic operator in a planar domain with a point interaction. It is of a geometric nature that the approximating family consists of operators with the same symbol and regular ...
D. I. Borisov, P. Exner
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Approximation of solutions to integro-differential time fractional wave equations in $ L^{p}- $space
Networks and Heterogeneous Media, 2023 In this paper, we investigate the abstract integro-differential time-fractional wave equation with a small positive parameter $ \varepsilon $. The $ L^{p}-L^{q} $ estimates for the resolvent operator family are obtained using the Laplace transform, the ...
Yongqiang Zhao, Yanbin Tang
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Fractal and Fractional, 2023 Fractional integrodifferential diffusion equations play a significant role in describing anomalous diffusion phenomena. In this paper, we study the existence and uniqueness of mild solutions to these equations.
Jia Mu, Zhiyuan Yuan, Yong Zhou
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Operators in Rigged Hilbert spaces: some spectral properties [PDF]
, 2013 A notion of resolvent set for an operator acting in a rigged Hilbert space $\D \subset \H\subset \D^\times$ is proposed. This set depends on a family of intermediate locally convex spaces living between $\D$ and $\D^\times$, called interspaces.
Bellomonte, G. +2 more
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