Journal ArticleDOI
A New Class of White Noise Generalized Functions
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TLDR
In this paper, the S-transform is studied as a mapping from a space of tensors to a space over a complex space, and the range of this transform is characterized in terms of analyticity and growth.Abstract:
The S-transform is studied as a mapping from a space of tensors to a space of functions over a complex space. The range of this transform is characterized in terms of analyticity and growth. These results are applied to a broad class of generalized functions in white noise analysis. These correspond to completions of the Gaussian L2-space which preserve orthogonality of Hermite polynomials. The S-transform is defined for the new generalized functions, and the range of this S-transform is identified in terms of analyticity and growth. Examples of the new spaces of generalized functions are given; these include distributions considered by Kondratiev and Streit, as well as new classes of distributions whose S-transforms have growth bounded by iterated exponentials.read more
Citations
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Journal ArticleDOI
Un théorème de dualité entre espaces de fonctions holomorphes à croissance exponentielle
TL;DR: In this article, the Laplace transform realizes a topological isomorphism of the strong dual of F θ (N ) on G θ * (N) on [0, ∞+∞[.
Journal ArticleDOI
Approximating Infinity-Dimensional Stochastic Darcy's Equations without Uniform Ellipticity
Juan Galvis,Marcus Sarkis +1 more
TL;DR: A stochastic Darcy's pressure equation whose coefficient is generated by a white noise process on a Hilbert space employing the ordinary (rather than the Wick) product using Wiener-Chaos finite element methods is considered.
Journal ArticleDOI
Analytic characterization of generalized fock space operators as two-variable entire functions with growth condition
TL;DR: In this article, a proper space is found for a solution to a normal-ordered white noise differential equation having highly singular coefficients, where the singular coefficients characterize the symbols of generalized Fock space operators.
Journal ArticleDOI
Quantum Stochastic Analysis via White Noise Operators in Weighted Fock Space
TL;DR: In this paper, a normal-ordered white noise differential equation with higher powers or higher order derivatives of quantum white noises is introduced and its regularity properties are investigated by means of weighted Fock spaces interpolating spaces of white noise distributions.
Book ChapterDOI
Bell Numbers, Log-Concavity, and Log-Convexity
TL;DR: In this article, it was shown that the Bell numbers of order k are log-concave, and the sequence of positive numbers with α(0) = 1 is a Bell number.
References
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Book
White noise distribution theory
TL;DR: In this article, the S-Transform has been used for the construction of test and generalized functions in a Hilbert space and an operator's Hilbert space, as well as a construction from a Hilbert Space and an Operator.
Journal ArticleDOI
Introduction to Algebraic and Constructive Quantum Field Theory
TL;DR: In this article, the authors present a rigorous treatment of the first principles of the algebraic and analytic core of quantum field theory and correlate modern mathematical theory with the explanation of the observed process of particle production and of particle-wave duality.
Journal ArticleDOI
A Characterization of Hida Distributions
TL;DR: In this paper, the space (S ∗ of Hida distributions is characterized in terms of analytic properties of the Fourier transformation of its elements, and the space is characterized by the Fouriers transformation of the elements.