On the Determinacy of the Moment Problem for Symmetric Algebras of a Locally Convex Space

Infusino, Maria; Kuhlmann, Salma; Marshall, Murray

doi:10.1007/978-3-319-62527-0_7

Cited by 9 publications

(10 citation statements)

References 17 publications

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“…We will refer to Conditions (1) and (2) combined as determining condition following the notation of [22], [24] and [25]. For a comparison between the determining condition, the infinite dimensional version of Carleman's condition and the other conditions appearing in [18] see [24,Remark 3.2].…”

Section: The Moment Problem On Symmetric Algebras Of Lc Real Spacesmentioning

confidence: 99%

“…For a comparison between the determining condition, the infinite dimensional version of Carleman's condition and the other conditions appearing in [18] see [24,Remark 3.2]. In particular, if L is τ -continuous then L is determining (see [14,Remark 6.2,(9)- (10)] for more details).…”

Section: The Moment Problem On Symmetric Algebras Of Lc Real Spacesmentioning

confidence: 99%

“…Several questions remain open also in relation to the determinacy of the moment problem on the symmetric algebra of a locally convex space as described in [24] (see also [22] for a review about determinacy in both finite and infinite dimensions). Last but not least, one could obviously ask: Question 3.14.…”

Section: The Moment Problem On Symmetric Algebras Of Lc Real Spacesmentioning

confidence: 99%

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Infinite dimensional moment problem: open questions and applications

Infusino¹,

Kuhlmann²

2017

Ordered Algebraic Structures and Related Topics

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This paper is dedicated to Murray Marshall, who posed many of the questions here addressed and was still working on them in the very last days of his life. We lost a wonderful collaborator and a dear friend. We sorely miss him.Abstract. Infinite dimensional moment problems have a long history in diverse applied areas dealing with the analysis of complex systems but progress is hindered by the lack of a general understanding of the mathematical structure behind them. Therefore, such problems have recently got great attention in real algebraic geometry also because of their deep connection to the finite dimensional case. In particular, our most recent collaboration with Murray Marshall and Mehdi Ghasemi about the infinite dimensional moment problem on symmetric algebras of locally convex spaces revealed intriguing questions and relations between real algebraic geometry, functional and harmonic analysis. Motivated by this promising interaction, the principal goal of this paper is to identify the main current challenges in the theory of the infinite dimensional moment problem and to highlight their impact in applied areas. The last advances achieved in this emerging field and briefly reviewed throughout this paper led us to several open questions which we outline here.

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Section: The Moment Problem On Symmetric Algebras Of Lc Real Spacesmentioning

confidence: 99%

Section: The Moment Problem On Symmetric Algebras Of Lc Real Spacesmentioning

confidence: 99%

Section: The Moment Problem On Symmetric Algebras Of Lc Real Spacesmentioning

confidence: 99%

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Infinite dimensional moment problem: open questions and applications

Infusino¹,

Kuhlmann²

2017

Ordered Algebraic Structures and Related Topics

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“…Recently, the stochastic epidemic models are increasingly investigated by many authors (Zhou and Zhang, 2016;Zhang et al, 2017;Liu et al, 2020;Seraphin Djaoue et al, 2020;Applebaum, 2009;Duan, 2015;Bao and Zhang, 2017;Tilahun et al, 2020;Tesfay et al, 2020) and different methods are adopted for the solution of non-linear systems in integer and fractional order see (Abbasbandy et al, 2017;Arqub, 2019;Joachimiak, 2020;Alchikh and Khuri, 2019;Bougoffa et al, 2016;Djilali, 2019;Djilali, 2018;Djilali, 2020a;Djilali, 2020b;Djilali et al, XXXX;Bentout et al, 2021;Djilali and Ghanbari, 2021). Moreover, moment closure techniques, supported by precise determinacy criteria and evolutive partial differential equations, are as well suitable instruments used in the analysis of similar systems see (Feng and Jin, 2018;Infusino and Kuna, 2020;Infusino et al, 2021;Li et al, 2019;Li and Viglialoro, 2021;Viglialoro and Woolley, 2020). Motivated by the above research studies, the main object of this study is to establish how the dynamics behaviors are affected by the environmental noise, i.e.…”

Section: Introductionmentioning

confidence: 99%

A stability analysis on a smoking model with stochastic perturbation

Zeb

Kumar

Tesfay

et al. 2021

HFF

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Purpose The purpose of this paper is to investigate the effects of irregular unsettling on the smoking model in form of the stochastic model as in the deterministic model these effects are neglected for simplicity. Design/methodology/approach In this research, the authors investigate a stochastic smoking system in which the contact rate is perturbed by Lévy noise to control the trend of smoking. First, present the formulation of the stochastic model and study the dynamics of the deterministic model. Then the global positive solution of the stochastic system is discussed. Further, extinction and the persistence of the proposed system are presented on the base of the reproductive number. Findings The authors discuss the dynamics of the deterministic smoking model form and further present the existence and uniqueness of non-negative global solutions for the stochastic system. Some previous study’s mentioned in the Introduction can be improved with the help of obtaining results, graphically present in this manuscript. In this regard, the authors present the sufficient conditions for the extinction of smoking for reproductive number is less than 1. Research limitations/implications In this work, the authors investigated the dynamic stochastic smoking model with non-Gaussian noise. The authors discussed the dynamics of the deterministic smoking model form and further showed for the stochastic system the existence and uniqueness of the non-negative global solution. Some previous study’s mentioned in the Introduction can be improved with the help of obtained results, clearly shown graphically in this manuscript. In this regard, the authors presented the sufficient conditions for the extinction of smoking, if <1, which can help in the control of smoking. Motivated from this research soon, the authors will extent the results to propose new mathematical models for the smoking epidemic in the form of fractional stochastic modeling. Especially, will investigate the effective strategies for control smoking throughout the world. Originality/value This study is helpful in the control of smoking throughout the world.

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“…For more details about the uniqueness of the representing measure in this case see [19,Section 3]. x α i i ) ≤ max{L(x 2k 1 ), .…”

mentioning

confidence: 99%

Moment Problem for Symmetric Algebras of Locally Convex Spaces

Ghasemi

Infusino

Kuhlmann

et al. 2018

Integr. Equ. Oper. Theory

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It is explained how a locally convex (lc) topology τ on a real vector space V extends to a locally multiplicatively convex (lmc) topology τ on the symmetric algebra S(V ). This allows the application of the results on lmc topological algebras obtained by Ghasemi, Kuhlmann and Marshall to obtain representations of τ -continuous linear function-as integrals with respect to uniquely determined Radon measures µ supported by special sorts of closed balls in the dual space of V . The result is simultaneously more general and less general than the corresponding result of Berezansky, Kondratiev andŠifrin. It is more general because V can be any lc topological space (not just a separable nuclear space), the result holds for arbitrary 2d-powers (not just squares), and no assumptions of quasi-analyticity are required. It is less general because it is necessary to assume that L : S(V ) → R is τ -continuous (not just continuous on each homogeneous part of S(V )).Murray Marshall passed away in May 2015. He worked on this manuscript together with us until the very last days of his life. We lost a collaborator of many years and a wonderful friend. We sorely miss him. (M. Ghasemi, M. Infusino, S. Kuhlmann) 2010 Mathematics Subject Classification. Primary 44A60 Secondary 14P99.

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On the Determinacy of the Moment Problem for Symmetric Algebras of a Locally Convex Space

Cited by 9 publications

References 17 publications

Infinite dimensional moment problem: open questions and applications

Infinite dimensional moment problem: open questions and applications

A stability analysis on a smoking model with stochastic perturbation

Moment Problem for Symmetric Algebras of Locally Convex Spaces

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