Symmetry of Nonlinear Operators

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 1 July 2024 | Viewed by 7952

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School of Mathematical Sciences, College of Science and Technology, Wenzhou-Kean University, 88 Daxue Rd, Ouhai, Wenzhou 325060, China
Interests: fractional calculus; wavelet analysis; fractal geometry; applied functional analysis; dynamical systems; information theory; Shannon theory; antenna theory; image processing
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“Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania
Interests: leaks; multiple index martingales; stochastic processes; stochastic dominations; ergodicity coefficients; probabilistic inequalities; theory ruin; Bayesian statistics; credibility theory; generalized linear mod

Special Issue Information

Dear Colleagues,

In the last five decades, nonlinear operators have been found to be remarkably popular and important due mainly to several applications in numerous and widespread fields of mathematics, physics, engineering, etc. In particular, nonlinear operators are widely applied in electromagnetism, quantum mechanics, information theory, dynamical systems, etc. For instance, nonlinear functional analysis represents one of the most interesting research fields in contemporary mathematics. Several nonlinear operators find new reformulation in noncommutative geometry. In addition, nonlinear operators provide several tools for solving differential, integral, integro-differential equations, and modeling in mathematical physics. In the last twenty years, considerable attention has been paid to fractal operators. Several publications shows this interest, especially toward the link with wavelet analysis. Consequently, wavelet investigation of fractal operators represents one of the most interesting research topics in contemporary mathematics. In particular, the application of complex wavelets in fractal operators seems to be of independent interest. As a result, the link between this kind of nonlinear operator and wavelet analysis may thus open up new frontiers in research.

In this Special Issue, we invite and welcome review, expository, and original papers dealing with recent advances in nonlinear operators and, from a more general point of view, all theoretical and practical studies in mathematics, physics, and engineering focused on this topic.

The main topics of this Special Issue include (but are not limited to):

  1. Fractal operators and wavelet modeling;
  2. Noncommutative models and nonlinear operators;
  3. Symmetry of nonlinear special functions and real-world models;
  4. Nonlinear operators on C*-algebras;
  5. Leibniz algebras, fractional calculus, and symmetry in physics;
  6. Chaoticity and dynamical systems theory;
  7. Nonlinear models in applied science.

Dr. Emanuel Guariglia
Prof. Dr. Gheorghita Zbaganu
Guest Editors

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Keywords

  • fractal operator
  • wavelet expansion
  • noncommutative model
  • symmetry
  • chaoticity
  • quantum system
  • fractional calculus
  • dynamical system

Published Papers (6 papers)

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Research

16 pages, 310 KiB  
Article
Finite Chaoticity and Pairwise Sensitivity of a Strong-Mixing Measure-Preserving Semi-Flow
by Risong Li, Jingmin Pi, Yongjiang Li, Tianxiu Lu, Jianjun Wang and Xianfeng Ding
Axioms 2023, 12(9), 860; https://doi.org/10.3390/axioms12090860 - 7 Sep 2023
Viewed by 622
Abstract
Chaos is a common phenomenon in nature and social sciences. As is well known, chaos has multiple definitions, and there are both differences and connections between them. The unique properties of chaotic systems can be leveraged to address challenges in communication, security, data [...] Read more.
Chaos is a common phenomenon in nature and social sciences. As is well known, chaos has multiple definitions, and there are both differences and connections between them. The unique properties of chaotic systems can be leveraged to address challenges in communication, security, data processing, system analysis, and control across different domains. For semi-flows, this paper introduces two important concepts corresponding to discrete dynamical systems, finitely chaotic and pairwise sensitivity. Since Tent map and its induced suspended semi-flows both have these two properties, then these two concepts on the semi-flows have extensive and important applications and meanings in information security, finance, artificial intelligence and other fields. This paper extends the vast majority of corresponding results in discrete dynamical systems to semi-flows. Full article
(This article belongs to the Special Issue Symmetry of Nonlinear Operators)
16 pages, 329 KiB  
Article
On Some Inequalities for the Generalized Euclidean Operator Radius
by Mohammad W. Alomari, Gabriel Bercu, Christophe Chesneau and Hala Alaqad
Axioms 2023, 12(6), 542; https://doi.org/10.3390/axioms12060542 - 31 May 2023
Viewed by 854
Abstract
In the literature, there are many criteria to generalize the concept of a numerical radius; one of the most recent and interesting generalizations is the so-called generalized Euclidean operator radius, which reads: [...] Read more.
In the literature, there are many criteria to generalize the concept of a numerical radius; one of the most recent and interesting generalizations is the so-called generalized Euclidean operator radius, which reads: ωpT1,,Tn:=supx=1i=1nTix,xp1/p,p1, for all Hilbert space operators T1,,Tn. Simply put, it is the numerical radius of multivariable operators. This study establishes a number of new inequalities, extensions, and generalizations for this type of numerical radius. More precisely, by utilizing the mixed Schwarz inequality and the extension of Furuta’s inequality, some new refinement inequalities are obtained for the numerical radius of multivariable Hilbert space operators. In the case of n=1, the resulting inequalities could be considered extensions and generalizations of the classical numerical radius. Full article
(This article belongs to the Special Issue Symmetry of Nonlinear Operators)
8 pages, 282 KiB  
Article
A Remark on Weak Tracial Approximation
by Xiaochun Fang and Junqi Yang
Axioms 2023, 12(3), 242; https://doi.org/10.3390/axioms12030242 - 27 Feb 2023
Viewed by 836
Abstract
In this paper, we extend the notion of generalized tracial approximation to the non-unital case. An example of this approximation, which comes from dynamical systems, is also provided. We use the machinery of Cuntz subequivalence to work in this non-unital setting. Full article
(This article belongs to the Special Issue Symmetry of Nonlinear Operators)
17 pages, 337 KiB  
Article
Weakly and Nearly Countably Compactness in Generalized Topology
by Zuhier Altawallbeh, Ahmad Badarneh, Ibrahim Jawarneh and Emad Az-Zo’bi
Axioms 2023, 12(2), 122; https://doi.org/10.3390/axioms12020122 - 26 Jan 2023
Cited by 1 | Viewed by 1100
Abstract
We define the notions of weakly μ-countably compactness and nearly μ-countably compactness denoted by Wμ-CC and Nμ-CC as generalizations of μ-compact spaces in the sense of Csaśzaŕ generalized topological spaces. To obtain a more general setting, [...] Read more.
We define the notions of weakly μ-countably compactness and nearly μ-countably compactness denoted by Wμ-CC and Nμ-CC as generalizations of μ-compact spaces in the sense of Csaśzaŕ generalized topological spaces. To obtain a more general setting, we define Wμ-CC and Nμ-CC via hereditary classes. Using μθ-open sets, μ-regular open sets, and μ-regular spaces, many results and characterizations have been presented. Moreover, we use the properties of functions to investigate the effects of some types of continuities on Wμ-CC and Nμ-CC. Finally, we define soft Wμ-CC and Nμ-CC as generalizations of soft μ-compactness in soft generalized topological spaces. Full article
(This article belongs to the Special Issue Symmetry of Nonlinear Operators)
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12 pages, 291 KiB  
Article
2-Complex Symmetric Composition Operators on H2
by Lian Hu, Songxiao Li and Rong Yang
Axioms 2022, 11(8), 358; https://doi.org/10.3390/axioms11080358 - 23 Jul 2022
Cited by 4 | Viewed by 1135
Abstract
In this paper, we study 2-complex symmetric composition operators with the conjugation J, defined by Jf(z)=(f(z¯))¯, on the Hardy space H2. More precisely, we obtain the [...] Read more.
In this paper, we study 2-complex symmetric composition operators with the conjugation J, defined by Jf(z)=(f(z¯))¯, on the Hardy space H2. More precisely, we obtain the necessary and sufficient condition for the composition operator Cϕ to be 2-complex symmetric with J when ϕ is an automorphism of D. We also characterize 2-complex symmetric with J when ϕ is a linear fractional self-map of D. Full article
(This article belongs to the Special Issue Symmetry of Nonlinear Operators)
11 pages, 328 KiB  
Article
On the Semi-Group Property of the Perpendicular Bisector in a Normed Space
by Gheorghiță Zbăganu
Axioms 2022, 11(3), 125; https://doi.org/10.3390/axioms11030125 - 10 Mar 2022
Viewed by 1705
Abstract
Let (X,d) be a metric linear space and aX. The point a divides the space into three sets: Ha = {xX: d(0,x) < d(x,a)}, Ma [...] Read more.
Let (X,d) be a metric linear space and aX. The point a divides the space into three sets: Ha = {xX: d(0,x) < d(x,a)}, Ma = {xX: d(0,x) = d(x,a)} and La = {xX: d(0,x) > d(x,a)}. If the distance is generated by a norm, Ha is called the Leibnizian halfspace of a, Ma is the perpendicular bisector of the segment 0,a and La is the remaining set La = X\(HaMa). It is known that the perpendicular bisector of the segment [0,a] is an affine subspace of X for all aX if, and only if, X is an inner product space, that is, if and only if the norm is generated by an inner product. In this case, it is also true that if x,yLaMa, then x + yLaMa. Otherwise written, the set LaMa is a semi-group with respect to addition. We investigate the problem: for what kind of norms in X the pair (LaMa,+) is a semi-group for all aX? In that case, we say that “(X,.)has the semi-group property” or that “the norm . has the semi-group property”. This is a threedimensional property, meaning that if all the three-dimensional subspaces of X have it, then X also has it. We prove that for two-dimensional spaces, (La,+) is a semi-group for any norm, that (X,.) has the semi-group property if, and only if, the norm is strictly convex, and, in higher dimensions, the property fails to be true even if the norm is strictly convex. Moreover, studying the Lp norms in higher dimensions, we prove that the semi-group property holds if, and only if, p = 2. This fact leads us to the conjecture that in dimensions greater than three, the semi-group property holds if, and only if, X is an inner-product space. Full article
(This article belongs to the Special Issue Symmetry of Nonlinear Operators)
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