A New Class of White Noise Generalized Functions

Cochran, William G.; Kuo, Hui-Hsiung; Sengupta, Ambar N.

doi:10.1142/s0219025798000053

Cited by 38 publications

(59 citation statements)

References 4 publications

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“…Son dual topologique via la transformation de Laplace est l'espace G %* (N ), avec %*(x)= e x &x&1. Cet espace a e te introduit dans [1] comme e tant l'image par la T.C d'un certain espace de distributions formelles note [&] : * , sans pour autant donner la caracte risation de l'espace test associe . D'autre part, pour construire et caracte riser des espaces de distributions, on utilise dans [1] la fonction G : (t)= n # N (: n t n Ân !…”

Section: â(1and;)unclassified

Un théorème de dualité entre espaces de fonctions holomorphes à croissance exponentielle

Gannoun

Hachaichi

Ouerdiane

et al. 2000

Journal of Functional Analysis

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Soit %* la fonction conjugue e de % et G %* (N ) l'espace des fonctions holomorphes sur N et qui ve rifient: il existe p # N, m>0 et M 0 telle que:On de montre que la transforme e de Laplace re alise un isomorphisme topologique entre le dual fort de F % (N$) et G %* (N ). On donne ensuite des applications de ce re sultat aÁ l'analyse du bruit blanc. Academic PressLet N$ be the dual of a nuclear Fre chet space N and % a Young function on [0, + [. We define the space F % (N$) of holomorphic functions on N$ which satisfy: for all m>0 and p # N there exists K 0 such thatLet %* be the conjugate function of % and G %* (N ) the space of holomorphic functions on N which satisfy: there exists p # N, m>0 and M 0 such thatWe prove that the Laplace transform realizes a topological isomorphism of the strong dual of F %

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Section: â(1and;)unclassified

Un théorème de dualité entre espaces de fonctions holomorphes à croissance exponentielle

Gannoun

Hachaichi

Ouerdiane

et al. 2000

Journal of Functional Analysis

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“…we are lead to estimate the series (10.27) where B 2 (k − h) are the Bell numbers of order 2 as defined in [9]. Under this assumption denoting c := 16L, (10.28)…”

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confidence: 99%

A White-Noise Approach to Stochastic Calculus

Accardi

Волович

2001

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

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Abstract. During the past 15 years a new technique, called the stochastic limit of quantum theory, has been applied to deduce new, unexpected results in a variety of traditional problems of quantum physics, such as quantum electrodynamics, bosonization in higher dimensions, the emergence of the noncrossing diagrams in the Anderson model, and in the large-N-limit in QCD, interacting commutation relations, new photon statistics in strong magnetic fields, etc. These achievements required the development of a new approach to classical and quantum stochastic calculus based on white noise which has suggested a natural nonlinear extension of this calculus. The natural theoretical framework of this new approach is the white-noise calculus initiated by T. Hida as a theory of infinite-dimensional generalized functions. In this paper, we describe the main ideas of the white-noise approach to stochastic calculus and we show that, even if we limit ourselves to the first-order case (i.e. neglecting the recent developments concerning higher powers of white noise and renormalization), some nontrivial extensions of known results in classical and quantum stochastic calculus can be obtained. (2000): 60H40. Mathematics Subject Classification

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“…In [1,Section 3] and [3,8], the Bell numbers b n (k) of order n were applied to white noise distribution theory. The Bell numbers b 2 (n) of order 2 for n ≥ 0 are just the Bell numbers B n generated in (1.1).…”

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confidence: 99%

Generalizations of the Bell Numbers and Polynomials and Their Properties

Qi¹,

Niu²,

Lim³

et al. 2017

Preprint

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Abstract. In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers of the first and second kinds, construct determinantal and product inequalities for these generalizations with aid of properties of the completely monotonic functions, and derive the logarithmic convexity for the sequence of these generalizations.

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A New Class of White Noise Generalized Functions

Cited by 38 publications

References 4 publications

Un théorème de dualité entre espaces de fonctions holomorphes à croissance exponentielle

Un théorème de dualité entre espaces de fonctions holomorphes à croissance exponentielle

A White-Noise Approach to Stochastic Calculus

Generalizations of the Bell Numbers and Polynomials and Their Properties

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