Composition Operators Research Articles

Composition operators on de Branges–Rovnyak spaces associated to a rational (not inner) function

In this paper, we characterize the boundedness, the compactness and the Hilbert–Schmidt property for composition operators acting from a de Branges–Rovnyak space H(b) into itself, when b is a rational function in the closed unit ball of H∞ (but not a finite Blaschke product). In particular, we extend some of the results obtained by D. Sarason and J.N. Silva in the context of local Dirichlet spaces.

Reprint of: On spaceability of shift-like operators on Lp

We prove the spaceability of the set of hypercyclic vectors for shift-like operators. Shift-like operators appear naturally as composition operators on Lp(X), when the underlying space X is dissipative. In the process of proving the main theorem, we provide, among other results of independent interest, a characterization of weakly mixing dissipative composition operators of bounded distortion.

Polynomial differentiation composition operators from Besov‐type spaces into Bloch‐type spaces

We give some characterizations for the boundedness, compactness, and essential norm of some Stević–Sharma‐type operators called the polynomial differentiation composition operators from Besov‐type spaces into Bloch‐type spaces on the unit disk.

Compact linear combination of composition operators on the weighted Bergman spaces

It is well-known that the research of linear combination of composition operators has become a topic of increasing interest. Recently, Choe, Koo and Wang proved that the compactness of combinations composition operators induced by the symbols satisfying the condition (CNC) implies that each difference is compact on the weighted Bergman space. Motivated by that work, in this paper, we discuss which difference is compact on the weighted Bergman space when the coefficients do not satisfy the condition (CNC).

Rough set approach to predict biochar stability and pH from pyrolysis conditions and feedstock characteristics

Biochar has gained increasing attention as a potential adsorbent for the sequestration of carbon dioxide (CO2) and enhancement of soil fertility. Biochar pH and stability are important adsorbent properties as they indicate the affinity of biochar for CO2 and its potential to be applied in soil for long periods. These attributes are influenced by the feedstock composition and pyrolysis conditions. Therefore, it is important to develop a model that can elucidate the underlying trends and inherent relationships between feedstock composition and pyrolysis operating parameters on biochar pH and stability. In this work, rough set machine learning (RSML) tools have been used to develop a model to quantify this relationship because of the interpretable nature of RSML. RSML is a rule-based prediction model that categorizes the biochar properties by utilizing ‘if. then’ rules to conditional attributes. In this study, the feedstock properties such as elemental (carbon, hydrogen, oxygen and nitrogen) composition, fixed carbon, ash content, volatile matter, and operating conditions such as residence time, heating rate, and temperature were the conditional attributes while pH, ash content and O/C ratio of biochar were considered the decision attributes. The rules generated from RSML were validated and evaluated for scientific coherency. Thus, this approach provided a model which could reflect on the physical phenomena at varying process conditions. As a result, it was recommended that the pyrolysis temperature is in between 375 and 475 °C, the ash content in the feedstock is between 2.59 and 3.55 wt% and volatile matter in the feedstock is in between 68.9 and 73.8 wt% to obtain biochar with minimum ash content (0–5 wt%), minimum O/C ratio (0–0.2), and high pH (9−11).

Ces\`{a}ro-Type Operator on the Dirichlet Space of the Upper Half Plane

We construct a Ces\`{a}ro-type operator acting on Dirichlet space of the upper half plane using the approach of strongly continuous semigroups of composition operators on Banach spaces. We then determine the spectral and norm properties of the obtained Ces\`{a}ro-type operator.

Counting functions for Dirichlet series and compactness of composition operators

AbstractWe give a sufficient condition for a composition operator with positive characteristic to be compact on the Hardy space of Dirichlet series.

Didactic Tool Based on Virtual and Augmented Reality in Art Education: Learning through an Interactive Game

This article presents research on the results of using a didactic tool based on virtual and augmented reality, developed for solving tasks from the field of spatial design. The theoretical part presents the context of the tool’s development and discusses spatial perception in new media, spatial design of images and screen views, and new media and augmented reality in school practice. The didactic tool consists of a computer, a computer screen, a computer camera, and a set of markers with symbols for different architectural elements that allow different composition operations. Manipulation of the markers is captured by a computer camera, which recognizes the symbols as function keys and allows interaction with a computer program. The computer decodes the data and displays it on the screen as surfaces and solids. This strategy promotes learning like a computer game. We tested it with eighth grade elementary students. The goal was to determine the extent to which the tool would affect the implementation of artistic tasks, creativity, motivation, satisfaction, and understanding of art concepts. The results presented here are encouraging, especially in the area of creativity, which was confirmed by teachers and students after the evaluation.

Boundedness and compactness of weighted composition operators and monomial operators

This paper characterises the boundedness and compactness of Agler–McCarthy monomial operators by reducing them to weighted composition operators and deriving explicit Carleson measure criteria on the half-plane. The results are illustrated by examples.

Composite scalar bosons masses: Effective potential versus Bethe-Salpeter approach

Ten years ago the 125 GeV Higgs resonance was discovered at the LHC [1,2], if this boson is a fundamental particle or a particle composed of new strongly interacting particles is still an open question. If this is a composite boson there are still no signals of other possible composite states of this scheme, a possible solution to this problem was recently discussed in Refs. [30,31], where it is argued that the Higgs boson can be a composite dilaton [30]. In this work, considering an effective potential for composite operators we verify that the potential responsible for a light composite scalar boson of O(120) GeV, behaves like ∝Φ4 suggesting that if the Higgs boson is a composite scalar it may be a composite dilaton.

Topological structure of the space of composition operators on $$L^{\!\infty }$$ of an unbounded, locally finite metric space

Topological structure of the space of composition operators on $$L^{\!\infty }$$ of an unbounded, locally finite metric space

A Riemann-Hilbert approach to Fredholm determinants of Hankel composition operators: Scalar-valued kernels

We characterize Fredholm determinants of a class of Hankel composition operators via matrix-valued Riemann-Hilbert problems, for additive and multiplicative compositions. The scalar-valued kernels of the underlying integral operators are not assumed to display the integrable structure known from the seminal work of Its, Izergin, Korepin and Slavnov [42]. Yet we are able to describe the corresponding Fredholm determinants through a naturally associated Riemann-Hilbert problem of Zakharov-Shabat type by solely exploiting the kernels' Hankel composition structures. We showcase the efficiency of this approach through a series of examples, we then compute several rank one perturbed determinants in terms of Riemann-Hilbert data and finally derive Akhiezer-Kac asymptotic theorems for suitable kernel classes.

Bounded below composition operators on the space of Bloch functions on the unit ball of a Hilbert space

Let B_E be the open unit ball of a complex finite or infinite dimensional Hilbert space E and consider the space mathcal {B}(B_E) of Bloch functions on B_E. Using Lipschitz continuity of the dilation map on B_E given by x mapsto (1-Vert xVert ^2) mathcal {R}f(x) for x in B_E, where mathcal {R}f denotes the radial derivative of f in mathcal {B}(B_E), we study when a composition operator on mathcal {B}(B_E) is bounded below.

Monoidal Width

We introduce monoidal width as a measure of complexity for morphisms in monoidal categories. Inspired by well-known structural width measures for graphs, like tree width and rank width, monoidal width is based on a notion of syntactic decomposition: a monoidal decomposition of a morphism is an expression in the language of monoidal categories, where operations are monoidal products and compositions, that specifies this morphism. Monoidal width penalises the composition operation along ``big'' objects, while it encourages the use of monoidal products. We show that, by choosing the correct categorical algebra for decomposing graphs, we can capture tree width and rank width. For matrices, monoidal width is related to the rank. These examples suggest monoidal width as a good measure for structural complexity of processes modelled as morphisms in monoidal categories.

EMA Health Indicator Extraction Based on Improved Multivariate State Estimation Technique With a Composite Operator

EMA Health Indicator Extraction Based on Improved Multivariate State Estimation Technique With a Composite Operator

Multifidelity deep operator networks for data-driven and physics-informed problems

Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either from experiments or simulations. In this work, we present a composite Deep Operator Network (DeepONet) for learning using two datasets with different levels of fidelity to accurately learn complex operators when sufficient high-fidelity data is not available. Additionally, we demonstrate that the presence of low-fidelity data can improve the predictions of physics-informed learning with DeepONets. We demonstrate the new multi-fidelity training in diverse examples, including modeling of the ice-sheet dynamics of the Humboldt glacier, Greenland, using two different fidelity models and also using the same physical model at two different resolutions.

Composite operators of stochastic model A

Composite operators of stochastic model A

Compositional Verification in Rewriting Logic

AbstractIn previous work, summarized in this paper, we proposed an operation of parallel composition for rewriting-logic theories, allowing compositional specification of systems and reusability of components. The present paper focuses on compositional verification. We show how the assume/guarantee technique can be transposed to our setting, by giving appropriate definitions of satisfaction based on transition structures and path semantics. We also show that simulation and equational abstraction can be done componentwise. Appropriate concepts of fairness and deadlock for our composition operation are discussed, as they affect satisfaction of temporal formulas. We keep in parallel a distributed and a global view of composed systems. We show that these views are equivalent and interchangeable, which may help our intuition and also has practical uses as, for example, it allows global-style verification of a modularly specified system. Under consideration in Theory and Practice of Logic Programming (TPLP).

On a linear operator between weighted‐type spaces of analytic functions

We characterize the boundedness, compactness, and estimate essential norm of the polynomial differentiation composition operator between weighted‐type spaces of analytic functions, in terms of the operator symbols and weights.

Multipoint correlators on the supersymmetric Wilson line defect CFT. Part II. Unprotected operators

We continue our study of multipoint correlators of scalar fields on the 1d defect CFT generated by inserting operators along the Maldacena-Wilson line in mathcal{N} = 4 SYM. We present a weak-coupling recursion relation that captures correlators at next-to-leading order involving an arbitrary number of the elementary scalar fields ϕi and ϕ6, the latter being unprotected. We can then build correlators of composite operators by pinching the scalar fields together. As a demonstration of our method, we give explicit results for correlators containing up to six points. We also expand some selected correlators using recently obtained conformal blocks in the comb and snowflake channel, and check that the extracted low-lying CFT data is consistent with explicit computations.