Generalized Brownian functionals and the Feynman integral
Ludwig Streit,Takeyuki Hida +1 more
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TLDR
In this article, a sufficiently rich class of nonlinear functionals of white noise, e.g., the Wiener process, were obtained by studying riggings of the L 2 space with the white noise measure.About:
This article is published in Stochastic Processes and their Applications.The article was published on 1984-01-01 and is currently open access. It has received 110 citations till now. The article focuses on the topics: Wiener process & White noise.read more
Citations
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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.
Journal ArticleDOI
Generalized Functionals in Gaussian Spaces: The Characterization Theorem Revisited☆
TL;DR: Gel'fand triples of test and generalized functionals in Gaussian spaces were constructed and characterized in this article, where the triples were constructed from test functions and generalized functions.
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Generalized Poisson Functionals
TL;DR: In this article, generalized Poisson functions are defined and analyzed with the aim of treating nonlinear systems with inputs being discrete and outputs being generalized functions, where the transformations and renormalization play essential roles.
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Analytic version of test functionals, Fourier transform, and a characterization of measures in white noise calculus
TL;DR: In this paper, it was shown that the space (J) of test white noise functionals has an analytic version A∞ which is an algebra as well as a topological linear space topologized by the projective limit of a sequence {Ap:pϵN} of Banach spaces with respective norm given by ∥ƒ∥Ap=supZϵCJ−p{|ƒ(z)|exp[−2−1∥z∥]p2]}, where SJ−p denotes the complexification of J−
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The Feynman integrand as a Hida distribution
TL;DR: In this article, it was shown that Feynman integrals are weighted averages over Brownian paths, with suitable Hida distributions as (complex) weights, for simple cases, the construction of these distributions is be performed explicitly, for a much larger class of interactions, their existence is shown.
References
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Journal ArticleDOI
Space-Time Approach to Non-Relativistic Quantum Mechanics
TL;DR: In this paper, the authors formulated non-relativistic quantum mechanics in a different way and showed that the probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way.
Book
Mathematical theory of Feynman path integrals
TL;DR: The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976, and an entire new chapter on the current forefront of research has been added.
Book ChapterDOI
Analysis of brownian functionals
TL;DR: In this paper, functionals of Brownian motion are expressed as functions of white noise and generalized to generalized functionals by expressing them as functions in the integral representation of the functionals.