NEW TOPOLOGICAL C-ALGEBRAS WITH APPLICATIONS IN LINEAR SYSTEMS THEORY

被引:5
|
作者
Alpay, Daniel [1 ]
Salomon, Guy [1 ]
机构
[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel
关键词
Nuclear spaces; topological rings; Wick product; convolution; white noise space; Vage inequality; Schwartz space of tempered distributions; Kondratiev spaces; linear systems on commutative rings;
D O I
10.1142/S0219025712500117
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Motivated by the Schwartz space of tempered distributions l' and the Kondratiev space of stochastic distributions S-1 we define a wide family of nuclear spaces which are increasing unions of (duals of) Hilbert spaces H-p', p is an element of N, with decreasing norms parallel to.parallel to(p). The elements of these spaces are functions on a free commutative monoid. We characterize those rings in this family which satisfy an inequality of the form parallel to f * g parallel to (p) <= A(p - q) parallel to f parallel to(q) parallel to g parallel to(p) for all p >= q + d, where * denotes the convolution in the monoid, A(p - q) is a strictly positive number and d is a fixed natural number (in this case we obtain commutative topological C-algebras). Such an inequality holds in S-1, but not in l'. We give an example of such a ring which contains l'. We characterize invertible elements in these rings and present applications to linear system theory.
引用
收藏
页数:30
相关论文
共 50 条
  • [21] EPIMORPHISMS OF C-ALGEBRAS ARE SURJECTIVE
    HOFMANN, KH
    NEEB, KH
    ARCHIV DER MATHEMATIK, 1995, 65 (02) : 134 - 137
  • [22] WEAKENING OF DEFINITION OF C-ALGEBRAS
    SEBESTYEN, Z
    ACTA SCIENTIARUM MATHEMATICARUM, 1973, 35 : 17 - 20
  • [23] PRIME C-ALGEBRAS AND ANTILATTICES
    ARCHBOLD, RJ
    PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1972, 24 (04) : 669 - &
  • [24] QUOTIENT STRUCTURES IN C-ALGEBRAS
    BLAU, HI
    JOURNAL OF ALGEBRA, 1995, 175 (01) : 24 - 64
  • [25] Boolean Algebra of C-Algebras
    Rao, Guddati C.
    Sundarayya, Perumali
    JOURNAL OF MATHEMATICAL AND FUNDAMENTAL SCIENCES, 2012, 44 (03) : 204 - 216
  • [26] Composition series in C-algebras
    Darafsheh, MR
    Barghi, AR
    ALGEBRA COLLOQUIUM, 1999, 6 (02) : 125 - 132
  • [27] TORSION UNITS OF INTEGRAL C-ALGEBRAS
    Herman, Allen
    Singh, Gurmail
    JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2015, 36 (02): : 141 - 155
  • [28] Morphisms and functor kerf in C-algebras
    Xu, Bangteng
    ALGEBRA COLLOQUIUM, 2008, 15 (01) : 145 - 166
  • [29] DISTRIBUTION AND SURVIVAL FUNCTIONS WITH APPLICATIONS IN INTUITIONISTIC RANDOM LIE C-ALGEBRAS
    Abdou, Afrah A. N.
    Cho, Yeol Je
    Saadati, Reza
    JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2016, 21 (02) : 345 - 354
  • [30] The K-groups and the index theory of certain comparison C-algebras
    Monthubert, Bertrand
    Nistor, Victor
    NONCOMMUTATIVE GEOMETRY AND GLOBAL ANALYSIS, 2011, 546 : 213 - +