scholarly journals Transfer of Fourier Multipliers into Schur Multipliers and Sumsets in a Discrete Group

2011 ◽  
Vol 63 (5) ◽  
pp. 1161-1187 ◽  
Author(s):  
Stefan Neuwirth ◽  
Éric Ricard
Keyword(s):  
Lebesgue Space ◽  
Discrete Group ◽  
Orlicz Spaces ◽  
Fourier Multipliers ◽  
Von Neumann ◽  
Riesz Projection ◽  
Schur Multipliers ◽  
Schauder Bases ◽  
The Relationship

Abstract We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue– Orlicz spaces of a discrete group and relative Toeplitz-Schur multipliers on Schatten–von- Neumann–Orlicz classes. Four applications are given: lacunary sets, unconditional Schauder bases for the subspace of a Lebesgue space determined by a given spectrum , the norm of the Hilbert transformand the Riesz projection on Schatten–von-Neumann classes with exponent a power of 2, and the norm of Toeplitz Schur multipliers on Schatten–von-Neumann classes with exponent less than 1.

The problem of measuring the quantity of output in the input–output model by W. Leontief in modeling the trends in economic reproduction of nations and regions

2021 ◽  
Vol 19 (8) ◽  
pp. 1568-1592
Author(s):  
Nikolai I. KURYSHEV
Keyword(s):  
Input Output ◽  
Von Neumann ◽  
Output Matrix ◽  
Production And Consumption ◽  
Production Quantity ◽  
Mathematical Analyses ◽  
Neumann Model ◽  
Product Output ◽  
The Relationship ◽  
Cost Characteristics

Subject. This article deals with the problem of constructing a Leontief's input–output matrix. Objectives. The article aims to determine the rules for constructing a Leontief's input–output matrix on the basis of data on production time and quantity of product output. Methods. For the study, I used the methods of logical and mathematical analyses. Results. The article formulates the rules for constructing a Leontief's input–output matrix, taking into account differences in the time of production, quantity of output, as well as the conditions for the reproduction of the resources expended. It summarizes these rules for the J. von Neumann model. Conclusions. The proposed approach to the analysis of the material mechanism of economic reproduction defines the relationship between the quantitative and cost characteristics of the production and consumption of products and resources. This relationship opens up new opportunities for the application of input–output models to create simple and accurate algorithms for identifying and predicting the macroeconomic trends.

scholarly journals Integral equations of the first kind of Sonine type

2003 ◽  
Vol 2003 (57) ◽  
pp. 3609-3632 ◽  
Author(s):  
Stefan G. Samko ◽  
Rogério P. Cardoso
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Lebesgue Space ◽  
Inverse Operator ◽  
Orlicz Spaces ◽  
Hypersingular Integral ◽  
The Real ◽  
Integrable Kernel

A Volterra integral equation of the first kindKφ(x):≡∫−∞xk(x−t)φ(t)dt=f(x)with a locally integrable kernelk(x)∈L1loc(ℝ+1)is called Sonine equation if there exists another locally integrable kernelℓ(x)such that∫0xk(x−t)ℓ(t)dt≡1(locally integrable divisors of the unit, with respect to the operation of convolution). The formal inversionφ(x)=(d/dx)∫0xℓ(x−t)f(t)dtis well known, but it does not work, for example, on solutions in the spacesX=Lp(ℝ1)and is not defined on the whole rangeK(X). We develop many properties of Sonine kernels which allow us—in a very general case—to construct the real inverse operator, within the framework of the spacesLp(ℝ1), in Marchaud form:K−1f(x)=ℓ(∞)f(x)+∫0∞ℓ′(t)[f(x−t)−f(x)]dtwith the interpretation of the convergence of this “hypersingular” integral inLp-norm. The description of the rangeK(X)is given; it already requires the language of Orlicz spaces even in the case whenXis the Lebesgue spaceLp(ℝ1).

Game Theory vs. Business Ethics

2015 ◽  
pp. 1849-1872
Author(s):  
Ben Tran
Keyword(s):  
Game Theory ◽  
Business Ethics ◽  
Emerging Economies ◽  
Moral Philosopher ◽  
John Von Neumann ◽  
Von Neumann ◽  
Economic Behaviour ◽  
History Of ◽  
The Moment ◽  
The Relationship

In 1954, the British philosopher Richard Braithwaite gave his inaugural lecture, Theory of Games as a Tool for the Moral Philosopher. Braithwaite predicted game theory would fundamentally change moral philosophy. However, in hindsight, John von Neumann and Oskar Morgenstern's publication of Theory of Games and Economic Behaviour was the moment modern game theory entered the discipline of ethics. The purpose of this chapter is to analyze the relationship between game theory and business ethics. In other words, this chapter explains how game theory plays a role in business ethics and affects business ethics for emerging economies and covers in detail: 1) the history of game theory; 2) types of/definition(s) of games; 3) business ethics; 4) business; and 5) ethics. The chapter concludes with the role that game theory and business ethics play in emerging economies.

Continuous Ergodic Extensions and Fibre Bundles

1978 ◽  
Vol 30 (02) ◽  
pp. 373-391 ◽  
Author(s):  
Robert J. Zimmer
Keyword(s):  
Real Line ◽  
Lebesgue Space ◽  
Transformation Group ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Von Neumann ◽  
Fibre Bundles ◽  
Direct Sum ◽  
Finite Dimensional ◽  
Measure Preserving Transformation

If a locally compact group G acts as a measure preserving transformation group on a Lebesgue space X, then there is a naturally induced unitary representation of G on L2(X), and one can study the action on X by means of this representation. The situation in which the representation has discrete spectrum (i.e., is the direct sum of finite dimensional representations) and the action is ergodic was examined by von Neumann and Halmos when G is the integers or the real line [7], and by Mackey for general non-abelian G [10].

scholarly journals Positive Herz–Schur multipliers and approximation properties of crossed products

2017 ◽  
Vol 165 (3) ◽  
pp. 511-532 ◽  
Author(s):  
ANDREW MCKEE ◽  
ADAM SKALSKI ◽  
IVAN G. TODOROV ◽  
LYUDMILA TUROWSKA
Keyword(s):  
Discrete Group ◽  
Crossed Products ◽  
Approximation Properties ◽  
Completely Positive ◽  
Haagerup Property ◽  
Schur Multipliers

For aC*-algebraAand a setXwe give a Stinespring-type characterisation of the completely positive SchurA-multipliers on κ(ℓ2(X)) ⊗A. We then relate them to completely positive Herz–Schur multipliers onC*-algebraic crossed products of the formA⋊α,rG, withGa discrete group, whose various versions were considered earlier by Anantharaman-Delaroche, Bédos and Conti, and Dong and Ruan. The latter maps are shown to implement approximation properties, such as nuclearity or the Haagerup property, forA⋊α,rG.

Do Prudent Agents Play Lotteries? Von Neumann's Contribution to the Theory of Rational Behavior

2006 ◽  
Vol 28 (1) ◽  
pp. 95-109 ◽  
Author(s):  
Nicola Giocoli
Keyword(s):  
Game Theory ◽  
Set Theory ◽  
100Th Anniversary ◽  
Economic Behavior ◽  
Rational Behavior ◽  
John Von Neumann ◽  
Von Neumann ◽  
Balanced Growth ◽  
The Relationship ◽  
Fixed Point Techniques

The year 2003 marked the 100th anniversary of the birth of John von Neumann (1903–1957), one of greatest geniuses of the last century. Beyond contributing to fields as diverse as set theory, quantum mechanics, atomic energy, and automatic computing, von Neumann has also had a decisive influence upon modern economics. From the invention of game theory to the axiomatization of expected utility, from the introduction of convex analysis and fixed-point techniques to the development of the balanced growth model, the von Neumann heritage can be clearly traced in several areas of our discipline. The aim of this paper is to clarify the relationship between the two concepts of rationality he devised in his classic 1944 book Theory of Games and Economic Behavior, written with the collaboration of the Austrian economist Oskar Morgenstern (von Neumann and Morgenstern 1953).

scholarly journals Fourier multipliers and group von Neumann algebras

2016 ◽  
Vol 354 (8) ◽  
pp. 766-770 ◽  
Author(s):  
Rauan Akylzhanov ◽  
Michael Ruzhansky
Keyword(s):  
Von Neumann Algebras ◽  
Fourier Multipliers ◽  
Von Neumann

scholarly journals SOFTWARE AND ALGORITHMIC PROVIDED FOR WORK WITH CELLULAR AUTOMATES

2018 ◽  
Vol 28 (3) ◽  
pp. 137-141
Author(s):  
O. V. Sinkevych ◽  
I. Ya. Sokolovskyy
Keyword(s):  
Cellular Automata ◽  
3D Model ◽  
Graphical Representation ◽  
Mathematical Functions ◽  
Von Neumann ◽  
Class System ◽  
First Order ◽  
3D Objects ◽  
The Relationship ◽  
Direct Use

In this paper, the system of initial theoretical positions is considered, which is the basis of the research search for variants of cellular automata for the study of thermal and mechanical processes in 3D objects of SolidWorks, through their representation in 2D von Neumann neighborhood of the first order. The execution of this work also involves the creation of initial rules for changing the investigated system, which are necessary for the direct use of cellular automata. As a result of the verification of these rules, it was found that their number may not be enough to address specific tasks in the field of 3D research. Because of this, it was left possible to create new rules for changing the system, or changes already existing. In addition, in the process of performing this work, all the processes of scientific research, as well as the proposed initial provisions have been repeatedly tested, developed and adjusted if necessary. For successful experiments, the 3D model under study was divided into 3D cubes of the same size. The number of these 3D cubes depends on the density of the section that the user specifies manually using the appropriate item of the developed software. In addition, in this paper describes the establishment of the relationship between the faces of created 3D cubes. These dependencies were presented in the form of an appropriate relationship scheme, which is then used in the design and configuration of the corresponding system classes, which are closely related to each word, both logically and functionally. Based on the developed system classes, appropriate software was created, which is the basis of the use of cellular automata in the study of tasks in the field of 3D modeling. In addition, in this paper a graphical representation of the interrelationships between the developed classes was presented. For a better understanding of the mechanism of the class system operation, a sequence diagram was developed. With this diagram, you can see not only how the classes interact with each other but also in what sequence this interaction takes place. In the future, this work involves expanding the capabilities of the software developed, as well as filling it with mathematical functions that would allow it to be used in the study of the mechanical and mechanical processes of various 3D objects.

Disjoint Hypercyclicity and Weighted Translations on Discrete Groups

2017 ◽  
Vol 60 (4) ◽  
pp. 712-720
Author(s):  
Chung-Chuan Chen
Keyword(s):  
Lebesgue Space ◽  
Discrete Group ◽  
Necessary Condition ◽  
Discrete Groups ◽  
Translation Operators ◽  
Weighted Translation ◽  
Sufficient And Necessary Condition ◽  
Disjoint Hypercyclicity

Let 1 ≤ p < ∞, and let G be a discrete group. We give a sufficient and necessary condition for weighted translation operators on the Lebesgue space ℓp(G) to be densely disjoint hypercyclic. The characterization for the dual of a weighted translation to be densely disjoint hypercyclic is also obtained.

On the Tensor Products of JW-Algebras

1995 ◽  
Vol 47 (4) ◽  
pp. 786-800 ◽  
Author(s):  
Fatmah B. Jamjoom
Keyword(s):  
Tensor Product ◽  
Von Neumann Algebra ◽  
Tensor Products ◽  
Von Neumann ◽  
The Relationship ◽  
Type Decomposition

AbstractIn this article we introduce and develop a theory of tensor products of JW-algebras. Since JW-algebras are so close to W*-algebras, one can expect that the W*-algebra tensor product theory will be actively involved. It is shown that if Mand N are JW-algebras with centres Z1 and Z2 respectively, then Z1 ⊗ Z2 is not the centre of the JW-tensor product JW() (see below for notation) ofMand N, in general. Also, the type decomposition of JW() has been determined in terms of the type decomposition of the JW-algebras M and N which, essentially, rely on the relationship between the types of the JW-algebra and the types of its universal enveloping Von Neumann algebra.

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