Composition Operator for Credal Sets Reconsidered

Author(s):  
Jiřina Vejnarová
2003 ◽  
Vol 45 (3) ◽  
pp. 351-358 ◽  
Author(s):  
David B. Pokorny ◽  
Jonathan E. Shapiro
Keyword(s):  

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 737
Author(s):  
Jelena D. Velimirovic ◽  
Aleksandar Janjic

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. More specifically, influence diagrams—as extended Bayesian network functions with interval probabilities represented through credal sets—were chosen for the predictive modelling scenario of replacing the most critical circuit breakers in optimal time. Namely, based on the available data on circuit breakers and other variables that affect the considered model of a complex power system, a group of experts was able to assess the situation using interval probabilities instead of crisp probabilities. Furthermore, the paper examines how the confidence interval width affects decision-making in this context and eliminates the information asymmetry of different experts. Based on the obtained results for each considered interval width separately on the action to be taken over the considered model in order to minimize the risk of the power system failure, it can be concluded that the proposed approach clearly indicates the advantages of using interval probability when making decisions in systems such as the one considered in this paper.


2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Piotr Budzyński

We construct an unbounded hyponormal composition operatorCϕinL2-space such that the domains ofCϕ2andCϕ2are trivial.


2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Guanghua He ◽  
Xi Fu ◽  
Hancan Zhu

We study Bloch-type spaces of minimal surfaces from the unit disk D into Rn and characterize them in terms of weighted Lipschitz functions. In addition, the boundedness of a composition operator Cϕ acting between two Bloch-type spaces is discussed.


1999 ◽  
Vol 42 (1) ◽  
pp. 97-103 ◽  
Author(s):  
E. G. Kwon

AbstractLet B = Bn be the open unit ball of Cn with volume measure v, U = B1 and B be the Bloch space on , 1 ≤ α < 1, is defined as the set of holomorphic f : B → C for whichif 0 < α < 1 and , the Hardy space. Our objective of this note is to characterize, in terms of the Bergman distance, those holomorphic f : B → U for which the composition operator defined by , is bounded. Our result has a corollary that characterize the set of analytic functions of bounded mean oscillation with respect to the Bergman metric.


2015 ◽  
Vol 62 (1) ◽  
pp. 1-12
Author(s):  
José A. Guerrero ◽  
Nelson Merentes ◽  
José L. Sánchez

Abstract In this paper we present the concept of total κ-variation in the sense of Hardy-Vitali-Korenblum for a real function defined in the rectangle Iab⊂R2. We show that the space κBV(Iab, R) of real functions of two variables with finite total κ-variation is a Banach space endowed with the norm ||f||κ = |f (a)| + κTV( f, Iab). Also, we characterize the Nemytskij composition operator H that maps the space of functions of two real variables of bounded κ-variation κBV(Iab, R) into another space of a similar type and is uniformly bounded (or Lipschitzian or uniformly continuous).


Author(s):  
Abraham Rueda Zoca

AbstractGiven two metric spaces M and N we study, motivated by a question of N. Weaver, conditions under which a composition operator $$C_\phi :{\mathrm {Lip}}_0(M)\longrightarrow {\mathrm {Lip}}_0(N)$$ C ϕ : Lip 0 ( M ) ⟶ Lip 0 ( N ) is an isometry depending on the properties of $$\phi $$ ϕ . We obtain a complete characterisation of those operators $$C_\phi $$ C ϕ in terms of a property of the function $$\phi $$ ϕ in the case that $$B_{{\mathcal {F}}(M)}$$ B F ( M ) is the closed convex hull of its preserved extreme points. Also, we obtain necessary condition for $$C_\phi $$ C ϕ being an isometry in the case that M is geodesic.


2010 ◽  
Vol 81 (3) ◽  
pp. 465-472
Author(s):  
CHENG YUAN ◽  
ZE-HUA ZHOU

AbstractWe investigate the composition operators Cφ acting on the Bergman space of the unit disc D, where φ is a holomorphic self-map of D. Some new conditions for Cφ to belong to the Schatten class 𝒮p are obtained. We also construct a compact composition operator which does not belong to any Schatten class.


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