Composition Operators Research Articles

Essential norm of linear operators from general weighted‐type spaces to Banach spaces and some applications

We present a result concerning the essential norm of linear operators mapping some general weighted‐type spaces of holomorphic functions on the open unit ball in to Banach spaces. As some applications, we compare essential norms of a product‐type operator of integral type and a weighted composition operator between some of the general weighted‐type spaces.

Anomalies and persistent order in the chiral Gross-Neveu model

We study the 2d chiral Gross-Neveu model at finite temperature T and chemical potential μ. The analysis is performed by relating the theory to a SU(N) × U(1) Wess-Zumino-Witten model with appropriate levels and global identifications necessary to keep track of the fermion spin structures. At μ = 0 we show that a certain ℤ2-valued ’t Hooft anomaly forbids the system to be trivially gapped when fermions are periodic along the thermal circle for any N and any T > 0. We also study the two-point function of a certain composite fermion operator which allows us to determine the remnants for T > 0 of the inhomogeneous chiral phase configuration found at T = 0 for any N and any μ. The inhomogeneous configuration decays exponentially at large distances for anti-periodic fermions while it persists for T > 0 and any μ for periodic fermions, as expected from anomaly considerations. A large N analysis confirms the above findings.

Schatten class composition operators on the Hardy space of Dirichlet series and a comparison-type principle

We give necessary and sufficient conditions for a composition operator with Dirichlet series symbol to belong to the Schatten classes S_{p} of the Hardy space \mathcal{H}^{2} of Dirichlet series. For p\geq 2 , these conditions lead to a characterization for the subclass of symbols with bounded imaginary parts. Finally, we establish a comparison-type principle for composition operators. Applying our techniques in conjunction with classical geometric function theory methods, we prove the analogue of the polygonal compactness theorem for \mathcal{H}^{2} and we give examples of bounded composition operators with Dirichlet series symbols on \mathcal{H}^{p} , p>0 .

Composition operators on weighted Fock spaces induced by $$A_{\infty }$$-type weights

Composition operators on weighted Fock spaces induced by $$A_{\infty }$$-type weights

Characterizations of Composition Operators on Bloch and Hardy Type Spaces

Characterizations of Composition Operators on Bloch and Hardy Type Spaces

Toeplitz operators and composition operators on the q-Bergman space

Toeplitz operators and composition operators on the q-Bergman space

ON THE CARTESIAN PRODUCT INTUITIONISTIC FUZZY RELATION

In this paper we study the intuitionistic fuzzy relation and the operations on the intuitionistic fuzzy relations. We first define theCartesian product of intuitionistic fuzzy sets, then introduce the projection and the cylindric extension of intuitionistic fuzzy relation and show the relation between them. The concept of a composition operator for the intuitionistic fuzzy relations, which represents a generalization for those of fuzzy sets is also discussed in this paper.

Difference of Weighted Composition Operators Over the Ball

Difference of Weighted Composition Operators Over the Ball

Analysis of Aging Characteristics of Umbrella Skirts of Composite Insulators Operating under the Influence of a Wind and Sand Environment in South Xinjiang.

To study the influence of multi-factors, such as long sunshine, sand erosion, and so on, in southern Xinjiang, we selected two kinds of composite insulators for the transmission lines in southern Xinjiang to study the aging characteristics of the umbrella skirt surface. The results of scanning electron microscope (SEM) and X-ray photoelectron spectroscopy (XPS) show that the surface roughness of the umbrella skirt is high and there are a large number of micron inorganic particles. The skirt has the characteristics of low C/O element ratio and high Al element content. The results of thermogravimetric analysis and micro infrared test show that the aging depth of the Myli Line skirt after 19 years of operation is 160~190 µm and that of Yuhe Line 1 after 14 years of operation is greater than 180 µm. The plasma discharge method was used to simulate the corona discharge in the actual operation to accelerate the aging of the surface of the umbrella skirt and the hydrophobic recovery of the umbrella skirt was investigated. The results show that the temperature has a great influence on the surface hydrophobic recovery performance after plasma treatment. These results may provide some theoretical guidance and technical support for the selection, operation, and maintenance of composite insulators in Xinjiang.

Fredholm weighted composition operators between weighted lp spaces: A simple process point of view

Abstract In this paper we analyze, from a mathematical point of view, a simple processes with input in l p ⁢ ( 𝐫 ) {l^{p}(\mathbf{r})} and output in l p ⁢ ( 𝐬 ) {l^{p}(\mathbf{s})} . We characterize the functions u : ℕ → ℂ {u:\mathbb{N}\to\mathbb{C}} and φ : ℕ → ℕ {\varphi:\mathbb{N}\to\mathbb{N}} which define weighted composition operators W φ , u {W_{\varphi,u}} having closed range when acting between two different weighted l p {l^{p}} spaces. We also analyze when this operator is upper or lower semi-Fredholm.

StructSim: Meta-Structure-Based Similarity Measure in Heterogeneous Information Networks

Similarity measures in heterogeneous information networks (HINs) have become increasingly important in recent years. Most measures in such networks are based on the meta path, a relation sequence connecting object types. However, in real-world scenarios, there exist many complex semantic relationships, which cannot be captured by the meta path. Therefore, a meta structure is proposed, which is a directed acyclic graph of object and relation types. In this paper, we explore the complex semantic meanings in HINs and propose a meta-structure-based similarity measure called StructSim. StructSim models the probability of subgraph expansion with bias from source node to target node. Different from existing methods, StructSim claims that the subgraph expansion is biased, i.e., the probability may be different when expanding from the same node to different nodes with the same type based on the meta structure. Moreover, StructSim defines the expansion bias by considering two types of node information, including out-neighbors of current expanded nodes and in-neighbors of next hop nodes to be expanded. To facilitate the implementation of StructSim, we further designed the node composition operator and expansion probability matrix with bias. Extensive experiments on DBLP and YAGO datasets demonstrate that StructSim is more effective than the state-of-the-art approaches.

Norm of the general polynomial differentiation composition operator from the space of Cauchy transforms to the mth weighted‐type space on the unit disk

We introduce the general polynomial differentiation composition operator where , , , are holomorphic functions on the open unit disk and , , are holomorphic self‐maps of , calculate norm of the operator acting from the space of Cauchy transforms to the th weighted‐type space, and characterize its boundedness, as well as the boundedness of the operator acting from the space of Cauchy transforms to the little th weighted‐type space.

Sharp inequalities for holomorphic function spaces

In this paper we establish some sharp inequalities for holomorphic Fock spaces in Cn and weighted Bergman spaces in the unit polydisk, which generalizes some results of Burbea. As an application, we prove Furdui's conjecture about the norm of composition operators between Fock spaces.

Weighted composition operators on spaces generated by fractional Cauchy kernels of the unit ball

Weighted composition operators on spaces generated by fractional Cauchy kernels of the unit ball

Harmonic Bloch Function Spaces and their Composition Operators

In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. In the sequel we investigate closed range composition operators. These results extends the similar results that were proven for composition operators on the Bloch spaces.

A study of the multipoint boundary value problem for nonlinear differential equations of arbitrary fractional order based on the fixed point theorem for composite nonlinear operators

Abstract The existence and distinctiveness of solutions, as well as the iterative approximations of the distinctive answer to the initial boundary value issue of nonlinear differential equations, may be solved with the help of the theory of nonlinear operators, which offers a strong theoretical guarantee and a fundamental tool. In this work, we examine the fixed point theory for composites nonlinear operators, which may offer a fresh approach to solving linear differential equations having arbitrary order fractional multipoint boundary value problems. The existing result of the boundary value issue’s solution is confirmed by the fixed point theorem for composites nonlinear operators, and the four-point boundary value problem for fractional-order linear equations of the Riemann-Liouville type is examined. A group of fractional-order nonlinear differential equations with deviating quantities are examined to examine the presence of an unusual positive solution for this boundary value problem. The existence of this unique positive solution is determined by the use of both the mixed monotone operator and the combined nonlinear operator fixed point theorem. Ultimately, the nonlinear Bagley-Torvik equation with a fractional order variable coefficient four-point boundary value problem is converted into a Fredholm-Hammerstein integral the formula of the second type with weakly singular or continuous kernels, and the fixed point principle is used to demonstrate the uniqueness of the solution in the space of continuous functions. Approximate solutions are provided for the second class of nonlinear Fredholm-Hammerstein integral equations with weakly singular kernels. The outcomes demonstrate the applicability and validity of the fixed point theorem to composite nonlinear operators, offering a fresh approach to solving the multipoint boundary value issue for nonlinear differential equations of any fractional order.

PARLE-G: Provable Automated Representation and Analysis Framework for Learnability Evaluation of Generic PUF Compositions

Besides enormous research efforts in the design of Physically Unclonable Functions (PUFs), its vulnerabilities are still being exploited using machine learning (ML) based model-building attacks. Due to inherent complicacy in exploring and manually converging to a strong PUF composition, the challenge of building ML-attack resistant PUFs continues. Hence, it becomes imperative to develop an automated framework that can formally assess the learnability of different PUF constructions and compositions to guide the designer to explore resilient PUFs. In this work, we present an automated analysis framework (PARLE-G), to formally represent and evaluate the Probably Approximately Correct (PAC) learnability of PUF constructions and their compositions. A high-level specification language PUF-G has been developed to structurally represent any PUF composition comprising a specified set of primitive components and composition operations. The tool takes a PUF design represented in PUF-G language as input and returns its PAC learnability result, identifying a suitable PAC learning algorithm and the PAC model parameters based on the input PUF design. PUF designs proven to be learnable by PARLE-G are segregated into different classes based on the asymptotic complexity of their learnability bounds. Such automated analysis helps a designer to make informed design choices, thereby strengthening a PUF construction from the architectural level.

Self-adjoint and hyponormal weighted composition operators on the Fock space

<p>One major aim of this paper is to characterize the self-adjointness of some special weighted composition operators on Fock space, and another major aim is to characterize the hyponormality of some composition operators on such space.</p>

General Transmutation Relations and Their Applications

We consider a very general class of fractional calculus operators, given by transmuting the classical fractional calculus along an arbitrary invertible linear operator S. Specific cases of S, such as shift, reflection, and composition operators, give rise to well-known settings such as that of fractional calculus with respect to functions, and allow simple connections between left-sided and right-sided fractional calculus with different constants of differintegration. We define, for the first time, general transmuted versions of the Laplace transform and convolution of functions, and discuss how these ideas can be used to solve fractional differential equations in more general settings.

Effects of fuel composition and vehicle operating temperature on in vitro toxicity of exhaust emissions

The study evaluates the impact of after-treatment systems, aromatic fuel content, and cold operating temperature on exhaust emission toxicity from vehicles complying with the Euro 6d emission regulation.