A unified characterization theorem in white noise theory

被引：17
|
作者：
Ji, UC [1 ]
Obata, N
机构：
[1] Chungbuk Natl Univ, Dept Math, Cheongju 361763, South Korea
[2] Tohoku Univ, Grad Sch Informat Sci, Sendai, Miyagi 9808579, Japan
来源：
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2003年 / 6卷 / 02期
关键词：
white noise theory; S-transform; operator symbol; Gateaux-entire function; Fock space;
D O I：
10.1142/S0219025703001122
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We revisit a CKS-space from the viewpoint of standard setup of white noise calculus and prove a general characterization theorem for white noise operators from a CKS-space into another CKS-space. The usual characterizations so far obtained for white noise distributions, white noise test functions and white noise operators are all consequences of the unified characterization theorem.
引用
收藏
页码：167 / 178
页数：12
相关论文
共 50 条
  • [41] A GENERALIZATION OF A THEOREM OF DENY WITH APPLICATIONS IN CHARACTERIZATION THEORY
    DAVIES, PL
    SHANBHAG, DN
    QUARTERLY JOURNAL OF MATHEMATICS, 1987, 38 (149): : 13 - 34
  • [42] The key theorem of learning theory about examples corrupted by noise
    Ha, MH
    Li, JH
    Li, J
    Wang, XZ
    PROCEEDINGS OF THE 2004 INTERNATIONAL CONFERENCE ON MACHINE LEARNING AND CYBERNETICS, VOLS 1-7, 2004, : 1911 - 1913
  • [43] White noise estimation theory based on Kalman filtering
    Deng, Zi-Li
    Xu, Yan
    2003, Science Press (29):
  • [44] Characteristics of response to nonstationary white noise. Theory
    Igusa, Takeru, 1904, (115):
  • [45] Effects of white noise on parametric resonance in λφ4 theory
    Ishihara, M
    PROGRESS OF THEORETICAL PHYSICS, 2005, 114 (01): : 157 - 177
  • [46] EXTERNAL NON-WHITE NOISE - THEORY AND EXPERIMENT
    SANCHO, JM
    MIGUEL, MS
    YAMAZAKI, H
    KAWAKUBO, T
    PHYSICA A, 1982, 116 (03): : 560 - 572
  • [47] A general fractional white noise theory and applications to finance
    Elliott, RJ
    van der Hoek, J
    MATHEMATICAL FINANCE, 2003, 13 (02) : 301 - 330
  • [48] White noise approach to interacting quantum field theory
    Huang, ZY
    Rang, GL
    RECENT DEVELOPMENTS IN STOCHASTIC ANALYSIS AND RELATED TOPICS, 2004, : 220 - 233
  • [49] Theory and practice of a fully controllable white noise generator
    Ionescu, FC
    CAS '96 PROCEEDINGS - 1996 INTERNATIONAL SEMICONDUCTOR CONFERENCE, 19TH EDITION, VOLS 1 AND 2, 1996, : 319 - 322
  • [50] A Unified Characterization of Private Learnability via Graph Theory
    Alon, Noga
    Moran, Shay
    Schefler, Hilla
    Yehudayoff, Amir
    THIRTY SEVENTH ANNUAL CONFERENCE ON LEARNING THEORY, 2023, 247
12345