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20 pages, 340 KiB

Open AccessArticle

A Study on Square-Mean S-Asymptotically Bloch Type Periodic Solutions for Some Stochastic Evolution Systems with Piecewise Constant Argument

by Mamadou Moustapha Mbaye, Amadou Diop and Gaston Mandata N’Guérékata

Mathematics 2025, 13(9), 1495; https://doi.org/10.3390/math13091495 - 30 Apr 2025

Viewed by 265

Abstract

This work is mainly focused on square-mean S-asymptotically Bloch type periodicity and its applications. The main aim of the paper is to introduce the definition of square-mean S-asymptotically Bloch type periodic processes with values in complex Hilbert spaces and systematically analyze [...] Read more.

This work is mainly focused on square-mean S-asymptotically Bloch type periodicity and its applications. The main aim of the paper is to introduce the definition of square-mean S-asymptotically Bloch type periodic processes with values in complex Hilbert spaces and systematically analyze some qualitative properties of this type of processes. These properties, combined with the inequality technique, evolution operator theory, fixed-point theory, and stochastic analysis approach, allow us to establish conditions for the existence and uniqueness of square-mean S-asymptotically Bloch type periodicity of bounded mild solutions for a class of stochastic evolution equations with infinite delay and piecewise constant argument. In the end, examples are given to illustrate the feasibility of our results. Full article

(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications III)

14 pages, 306 KiB

Open AccessArticle

On the Product of Weighted Composition Operators and Radial Derivative Operators from the Bloch-Type Space into the Bers-Type Space on the Fourth Loo-Keng Hua Domain

by Xiaoman Liu and Yongmin Liu

Mathematics 2024, 12(19), 3108; https://doi.org/10.3390/math12193108 - 4 Oct 2024

Viewed by 719

Abstract

Let

H E_{I V}

be the fourth Loo-Keng Hua domain. We study the boundedness of the product of the weighted composition operator and the radial derivative operator from the Bloch-type space

B^{α} (H E_{I V})

into the Bers-type [...] Read more.

Let

H E_{I V}

be the fourth Loo-Keng Hua domain. We study the boundedness of the product of the weighted composition operator and the radial derivative operator from the Bloch-type space

B^{α} (H E_{I V})

into the Bers-type space

A^{β} (H E_{I V})

and provide the necessary and sufficient conditions for their boundedness. Full article

24 pages, 362 KiB

Open AccessArticle

Boundedness and Compactness of Weighted Composition Operators from (α, k)-Bloch Spaces to

A

_(β,k) Spaces on Generalized Hua Domains of the Fourth Kind

by Jiaqi Wang and Jianbing Su

Axioms 2024, 13(8), 539; https://doi.org/10.3390/axioms13080539 - 8 Aug 2024

Cited by 1 | Viewed by 790

Abstract

This paper addresses the weighted composition operators

{}_{ψ}C_{ϕ}

from the

(α, k)

-Bloch spaces to the

A_{(β, k)}

spaces of bounded holomorphic functions on W, where W is a generalized Hua domain of the [...] Read more.

This paper addresses the weighted composition operators

{}_{ψ}C_{ϕ}

from the

(α, k)

-Bloch spaces to the

A_{(β, k)}

spaces of bounded holomorphic functions on W, where W is a generalized Hua domain of the fourth kind. Additionally, we obtain some necessary and sufficient conditions for the boundedness and compactness of these operators. Full article

(This article belongs to the Special Issue Recent Advances in Complex Analysis and Related Topics)

14 pages, 310 KiB

Open AccessArticle

Sums of Generalized Weighted Composition Operators from Weighted Bergman Spaces Induced by Doubling Weights into Bloch-Type Spaces

by Xiangling Zhu and Qinghua Hu

Axioms 2024, 13(8), 530; https://doi.org/10.3390/axioms13080530 - 5 Aug 2024

Viewed by 943

Abstract

The single generalized weighted composition operator

D_{u, ψ}^{n}

on various spaces of analytic functions has been investigated for decades, i.e.,

D_{u, ψ}^{n} f = u \cdot (f^{(n)} \circ ψ)

, where [...] Read more.

The single generalized weighted composition operator

D_{u, ψ}^{n}

on various spaces of analytic functions has been investigated for decades, i.e.,

D_{u, ψ}^{n} f = u \cdot (f^{(n)} \circ ψ)

, where

f \in H (D)

. However, the study of the finite sum of generalized weighted composition operators with different orders, i.e.,

P_{U, ψ}^{k} f = u_{0} \cdot f \circ ψ + u_{1} \cdot f^{'} \circ ψ + \dots + u_{k} \cdot f^{(k)} \circ ψ,

is far from complete. The boundedness, compactness and essential norm of sums of generalized weighted composition operators from weighted Bergman spaces with doubling weights into Bloch-type spaces are investigated. We show a rigidity property of

P_{U, ψ}^{k}

. Specifically, the boundedness and compactness of the sum

P_{U, ψ}^{k}

is equivalent to those of each

D_{u_{n}, ψ}^{n}

,

0 \leq n \leq k .

Full article

(This article belongs to the Section Mathematical Analysis)

27 pages, 361 KiB

Open AccessArticle

Boundedness and Compactness of Weighted Composition Operators from α-Bloch Spaces to Bers-Type Spaces on Generalized Hua Domains of the First Kind

by Jiaqi Wang and Jianbing Su

Mathematics 2023, 11(20), 4403; https://doi.org/10.3390/math11204403 - 23 Oct 2023

Cited by 4 | Viewed by 1171

Abstract

We address weighted composition operators

ψ C_{ϕ}

from

α

-Bloch spaces to Bers-type spaces of bounded holomorphic functions on Y, where Y is a generalized Hua domain of the first kind, and obtain some necessary and sufficient conditions for the boundedness and [...] Read more.

We address weighted composition operators

ψ C_{ϕ}

from

α

-Bloch spaces to Bers-type spaces of bounded holomorphic functions on Y, where Y is a generalized Hua domain of the first kind, and obtain some necessary and sufficient conditions for the boundedness and compactness of those operators. Full article

(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)

26 pages, 380 KiB

Open AccessArticle

On a Sum of More Complex Product-Type Operators from Bloch-Type Spaces to the Weighted-Type Spaces

by Cheng-Shi Huang and Zhi-Jie Jiang

Axioms 2023, 12(6), 566; https://doi.org/10.3390/axioms12060566 - 7 Jun 2023

Cited by 3 | Viewed by 1823

Abstract

The aim of the present paper is to completely characterize the boundedness and compactness of a sum operator defined by some more complex products of composition, multiplication, and mth iterated radial derivative operators from Bloch-type spaces to weighted-type spaces on the unit [...] Read more.

The aim of the present paper is to completely characterize the boundedness and compactness of a sum operator defined by some more complex products of composition, multiplication, and mth iterated radial derivative operators from Bloch-type spaces to weighted-type spaces on the unit ball. In some applications, the boundedness and compactness of all products of composition, multiplication, and mth iterated radial derivative operators from Bloch-type spaces to weighted-type spaces on the unit ball are also characterized. Full article

(This article belongs to the Special Issue Theory of Functions and Applications)

12 pages, 287 KiB

Open AccessArticle

Norms of a Product of Integral and Composition Operators between Some Bloch-Type Spaces

by Stevo Stević

Axioms 2023, 12(5), 491; https://doi.org/10.3390/axioms12050491 - 18 May 2023

Viewed by 1259

Abstract

We present some formulas for the norm, as well as the essential norm, of a product of composition and an integral operator between some Bloch-type spaces of analytic functions on the unit ball, in terms of given symbols and weights. Full article

(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)

23 pages, 1320 KiB

Open AccessEditor’s ChoiceArticle

Topological Classification of Correlations in 2D Electron Systems in Magnetic or Berry Fields

by Janusz E. Jacak

Materials 2021, 14(7), 1650; https://doi.org/10.3390/ma14071650 - 27 Mar 2021

Cited by 1 | Viewed by 2075

Abstract

Recent topology classification of 2D electron states induced by different homotopy classes of mappings of the planar Brillouin zone into Bloch space can be supplemented by a homotopy classification of various phases of multi-electron homotopy patterns induced by Coulomb interaction between electrons. The [...] Read more.

Recent topology classification of 2D electron states induced by different homotopy classes of mappings of the planar Brillouin zone into Bloch space can be supplemented by a homotopy classification of various phases of multi-electron homotopy patterns induced by Coulomb interaction between electrons. The general classification of such type is presented. It explains the topologically protected correlations responsible for integer and fractional Hall effects in 2D multi-electron systems in the presence of perpendicular quantizing magnetic field or Berry field, the latter in topological Chern insulators. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to local binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants and illustrated by experimental observations in GaAs 2DES, graphene monolayer, and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to the local crystal field, local disorder, and variation of the electron interaction strength. The nonzero interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems. Full article

(This article belongs to the Special Issue Topological Approaches to 2D Multielectron Correlated States)

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12 pages, 261 KiB

Open AccessArticle

Estimates on Some General Classes of Holomorphic Function Spaces

by Amnah E. Shammaky and Ahmed El-Sayed Ahmed

Symmetry 2021, 13(4), 528; https://doi.org/10.3390/sym13040528 - 24 Mar 2021

Viewed by 1736

Abstract

In this current manuscript, some general classes of weighted analytic function spaces in a unit disc are defined and studied. Special functions significant in both analytic

T (p, q, m, s; Ψ)

norms and analytic

Ψ

-Bloch [...] Read more.

In this current manuscript, some general classes of weighted analytic function spaces in a unit disc are defined and studied. Special functions significant in both analytic

T (p, q, m, s; Ψ)

norms and analytic

Ψ

-Bloch norms serve as a framework for introducing new families of analytic classes. An application in operator theory is provided by establishing important properties of the composition-type operator

C_{ϕ}

such as the boundedness and compactness with the help of the defined new classes. Full article

(This article belongs to the Special Issue Complex Analysis, in Particular Analytic and Univalent Functions)

19 pages, 455 KiB

Open AccessArticle

Some Classical and Quantum Aspects of Gravitoelectromagnetism

by Giorgio Papini

Entropy 2020, 22(10), 1089; https://doi.org/10.3390/e22101089 - 27 Sep 2020

Cited by 4 | Viewed by 2373

Abstract

It has been shown that, even in linear gravitation, the curvature of space-time can induce ground state degeneracy in quantum systems, break the continuum symmetry of the vacuum and give rise to condensation in a system of identical particles. Condensation takes the form [...] Read more.

It has been shown that, even in linear gravitation, the curvature of space-time can induce ground state degeneracy in quantum systems, break the continuum symmetry of the vacuum and give rise to condensation in a system of identical particles. Condensation takes the form of a temperature-dependent correlation over distances, of momenta oscillations about an average momentum, of vortical structures and of a positive gravitational susceptibility. In the interaction with quantum matter and below a certain range, gravity is carried by an antisymmetric, second order tensor that satisfies Maxwell-type equations. Some classical and quantum aspects of this type of “gravitoelectromagnetism” were investigated. Gravitational analogues of the laws of Curie and Bloch were found for a one-dimensional model. A critical temperature for a change in phase from unbound to isolated vortices can be calculated using an

X Y

-model. Full article

(This article belongs to the Special Issue Gravitomagnetism and Quantum Mechanics)

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