2 edition of **Complex white noise and infinite dimensional unitary group** found in the catalog.

Complex white noise and infinite dimensional unitary group

Takeyuki Hida

- 385 Want to read
- 6 Currently reading

Published
**1971**
by Mathematical Institute, Nagoya University in [Nagoya, Japan]
.

Written in English

- Gaussian processes.,
- Wiener integrals.,
- Linear algebraic groups.,
- Unitary groups.

**Edition Notes**

Bibliography: p. [51]

Statement | Takeyuki Hida. |

Classifications | |
---|---|

LC Classifications | QA274.4 .H5 |

The Physical Object | |

Pagination | [53] p. ; |

Number of Pages | 53 |

ID Numbers | |

Open Library | OL4926533M |

LC Control Number | 76352960 |

to work out a calculus of white noise functionals. II. Since we have the rotation group acting on an "infinite dimensional sphere", we may see a counterpart of the analysis on finite dimensional spheres. The unitary representation theory of Lie groups has given us valuable suggestions. The approach in this line is quite successful. In addition, we. Abstract: A simple axiomatic characterization of the general (infinite dimensional, noncommutative) Ito algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. The notion of Ito B*-algebra, generalizing the C*-algebra is defined to include the Banach infinite dimensional Ito algebras of quantum Brownian and quantum Levy motion, and the .

By TAKEYUKI HIDA, HUI‐HSUING KUO, JÜRGEN POTTHOFF and LUDWIG STREIT: pp., £, ISBN 0 9 (Kluwer, ). cannot exist a complex measure µon the space of continuous paths [0,∞) → Rm such that the ﬁnite dimensional distributions of µare given by the integral kernel exp(−itH 0,0)(x,y) of exp(−itH 0,0), showing that there cannot even exist 1 a path integral formula in the literal sense for the unitary group of the Laplace operator H 0,0.

The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. The wikipedia page on Lorentz Group Representations also gives the same argument, and it cites a physics paper (and a theorem in Hall's book which does not suffice) without further context. It is true that the group generated by the exponentials of a Lie Subalgebra has a unique structure of Lie Subgroup, but this need not be an embedded.

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On the other hand, the infinite dimensional unitary group arises naturally in the study of the probability measure determined on the complex-valued (generalised) function space by complex white noise.

This unitary group plays the same role here as the infinite-dimensional rotation group did in describing properties of white noise (§).Author: T. Hida. The other characteristic is that the white noise analysis has an aspect of infinite dimensional harmonic analysis arising from the infinite dimensional rotation group.

With the help of this rotation group, the white noise analysis has explored new areas of mathematics and has extended the fields of applications.

Sample Chapter(s). Complex White Noise and the Infinite Dimensional Unitary Group (T Hida) Complex Itô Formulas (M Redfern) White Noise Analysis: Background and a Recent Application (J Becnel & A N Sengupta) Probability Measures with Sub-Additive Principal Szegö–Jacobi Parameters (A Stan) Donsker's Functional Calculus and Related Questions (P-L Chow & J Potthoff).

[2] Hida, T., Complex white noise and infinite dimensional unitary group, lecture note, Nagoya University (). Zentralblatt MATH: [3] Brownian motion, Iwanami Publ.

Comp., Tokyo () (in Japanese, an English translation will appear in Springer-Verlag). Infinite dimensional rotation group and unitary group. It is well known that the ”infinite dimensional rotation group ” has naturally been introduced in connection with white noise, and the group describes certain invariance of the white noise measure.

Hence, we may say that the white noise analysis should have an aspect of an infinite. We discuss the infinite dimensional unitary group U(E c) in connection with complex white noise.

Some important subgroups of U(E c) enjoy a beautiful structure expressed in terms of Lie algebras, and they play significant probabilistic roles. Takeyuki Hida has written: 'Complex white noise and infinite dimensional unitary group' -- subject(s): Gaussian processes, Linear algebraic groups, Unitary groups, Wiener integrals 'Mathematical.

Since its inception in the nineteen seventies –, white noise analysis has developed into a viable framework for stochastic and infinite-dimensional analysis –, with a growing number of applications in various disciplines, most notably perhaps in quantum ally speaking, the role here of (Gaussian, continuous parameter) white noise — a generalized random process (cf.

1. Quantum control and the infinite-dimensional unitary group. Essentially infinite-dimensional transformations. To control the time evolution of quantum systems is an essential step in many applications of quantum the fields requiring accurate control of quantum mechanical evolution are quantum state engineering, cooling of molecular degrees of freedom, selective excitation.

This book treats the theory and applications of analysis and functional analysis in infinite dimensions based on white noise. By white noise we mean the generalized Gaussian process which is (informally) given by the time derivative of the Wiener process, i.e., by the velocity of Brownian mdtion.

Download Citation | Complex White Noise and Coherent State Representations | An infinite-dimensional extension of a coherent state representation is discussed within the framework of white noise. The article is devoted to the problem of Hilbert–Schmidt type analytic extensions in Hardy spaces over the infinite-dimensional unitary group endowed with an invariant probability measure.

In this paper we present examples of stochastic partial differential equations of the “multiplicative noise type” a rising from laser communication problems.

The basic origins and generic structure of these equations are described and their relation to general quantum estimation and filtering theory explained. Generalized white noise functionals --Elemental random variables and Gaussian processes --Linear processes and linear fields --Harmonic analysis arising from infinite dimensional rotation group --Complex white noise and infinite dimensional unitary group --Characterization of Poisson noise --Innovation theory --Variational calculus for random.

White Noise is the eighth novel by Don DeLillo, published by Viking Press in It won the U.S. National Book Award for Fiction. White Noise is an example of postmodern is widely considered DeLillo's "breakout" work and brought him to the attention of a much larger audience.

Complex white noise and the infinite dimensional unitary group / T. Hida --Complex Itô formulas / M. Redfern --White noise analysis: background and a recent application / J.

Becnel and A.N. Sengupta --Probability measures with sub-additive principal Szegö-Jacobi parameters / A. Stan --Donsker's functional calculus and related questions / P. The totality of states forms an infinite-dimensional complex linear space equipped with an indefinite inner product.

one is the first KMO-Langevin equation having a white noise as a random force and the other is It has been assumed that the irreducible unitary representations of the group sDiff R 3 are the quantum counterpart of the.

x Lectures on White Noise Functionals some elementary description is included. Beginners would nd it easy to follow the edi ce of white noise theory.

The present work, though far from claiming completeness, aims at giv-ing an outline of white noise analysis responding to. The essential part of the analysis comes from the white noise theory,which provides the main route of the analysis of functionals of the innovation.

Naturally, the analysis is infinite dimensional. Note that our analysis has a viewpoint of harmonic analysis arising from the infinite dimensional rotation group.

Prof. Kuo works on three areas in stochastic analysis: (1) White noise analysis, (2) Stochastic differential equations, and (3) Probability theory on infinite dimensional spaces.

For the third area, he wrote a very popular book in ``Gaussian measures in Banach spaces'' (Lecture Notes in Math., volumeSpringer-Verlag.). White noise approach to Gaussian random fields - Volume - Ke-Seung Lee. Skip to main content. We use cookies to distinguish you from other users and to provide you with a better experience on our websites.

Close this message to accept cookies or find out how to manage your cookie settings.Learn the basics of white noise theory with White Noise Distribution Theory. This book covers the mathematical foundation and key applications of white noise theory without requiring advanced knowledge in this area.

This instructive text specifically focuses on relevant application topics such as integral kernel operators, Fourier transforms, Laplacian operators, white noise integration.At first i will initialize my white noise generator with mean m=0 and sigma=10 (for example).

It will lead variance of generator to value N= So, after this i will generate two numbers from generator and this numbers will represent me real and imaginary part of complex noise sample with variance N=+=