𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Paley–Wiener Theorem for White Noise Analysis

✍ Scribed by Aurel Stan

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
178 KB
Volume
173
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis

Analogue results of the classical Paley Wiener theorems that characterize classes of functions with compact support in terms of their Fourier transform are given for some subspaces of square integrable functions over a white noise space. 2000

📜 SIMILAR VOLUMES

Paley–Wiener Theorems for Hyperbolic Spa
Paley–Wiener Theorems for Hyperbolic Spaces
✍ Nils Byrial Andersen 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 367 KB

We prove a topological Paley Wiener theorem for the Fourier transform defined on the real hyperbolic spaces SO o ( p, q)ÂSO o ( p&1, q), for p, q # 2N, without restriction to K-types. We also obtain Paley Wiener type theorems for L \_ -Schwartz functions (0<\_ 2) for fixed K-types.

The Paley–Wiener Theorem for the Hua Sys
The Paley–Wiener Theorem for the Hua System
✍ Richard Penney 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 162 KB

E. Damek, A. Hulanicki, and R. Penney (J. Funct. Anal., in press) studied a canonical system of differential equations (the Hua system) denoted HJK which is definable on any Ka hlerian manifold M. Functions annihilated by this system are called ``Hua-harmonic.'' In the case where M is a bounded homo

Paley-Wiener Type Theorems for Colombeau
Paley-Wiener Type Theorems for Colombeau′s Generalized Functions
✍ M. Nedeljkov; S. Pilipovic 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 460 KB

We define the Laplace transformation for elements of Colombeau's spaces \(\mathscr{\varphi}_{c}\left(\mathbf{R}^{n}\right), \mathscr{G}_{c}^{x}\left(\mathbf{R}^{n}\right)\) and \(\mathscr{G}_{1}(\Gamma)\), where \(\Gamma\) is a cone. We obtain, in Theorems 1,2 , and 4 , the "expected" Paley-Wiener t

The Paley–Wiener theorem for certain nil
The Paley–Wiener theorem for certain nilpotent Lie groupsJean
✍ Jean Ludwig; Carine Molitor–Braun 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 243 KB

## Abstract We generalize the classical Paley–Wiener theorem to special types of connected, simply connected, nilpotent Lie groups: First we consider nilpotent Lie groups whose Lie algebra admits an ideal which is a polarization for a dense subset of generic linear forms on the Lie algebra. Then we

The Paley–Wiener Theorem in Rn with the
The Paley–Wiener Theorem in Rn with the Clifford Analysis Setting
✍ Kit-Ian Kou; Tao Qian 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 139 KB

We prove the Paley-Wiener Theorem in the Clifford algebra setting. As an application we derive the corresponding result for conjugate harmonic functions.

Paley–Wiener-Type Theorems for a Class o
Paley–Wiener-Type Theorems for a Class of Integral Transforms
✍ Vu Kim Tuan; Ahmed I. Zayed 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 176 KB

A characterization of weighted L 2 I spaces in terms of their images under various integral transformations is derived, where I is an interval (finite or infinite). This characterization is then used to derive Paley-Wiener-type theorems for these spaces. Unlike the classical Paley-Wiener theorem, ou