Gaussian measures on linear spaces

1996 ◽  
Vol 79 (2) ◽  
pp. 933-1034 ◽  
Author(s):  
V. I. Bogachev
Keyword(s):  
Gaussian Measures ◽  
Linear Spaces

scholarly journals The Topological Support of Gaussian Measure in Banach Space

1975 ◽  
Vol 57 ◽  
pp. 59-63 ◽  
Author(s):  
N. N. Vakhania
Keyword(s):  
Banach Space ◽  
Probability Measure ◽  
Gaussian Measure ◽  
Separable Banach Space ◽  
Covariance Operator ◽  
Probability Measures ◽  
Gaussian Measures ◽  
Linear Spaces

The main result of the present paper is the theorem 1, which describes the topological support of an arbitrary Gaussian measure in a separable Banach space. This theorem will be proved after some discussion of the notion of support itself. But we begin with the reminder of the notion of covariance operator of a probability measure. This notion has a great importance not only for the description of support of Gaussian measures but also for the study of other problems in the theory of probability measures in linear spaces (c.f. [1], [2]).

Operator approach for orthogonality in linear spaces

2018 ◽  
Vol 11 (4) ◽  
pp. 103-112
Author(s):  
Mahdi Iranmanesh ◽  
Maryam Saeedi Khojasteh
Keyword(s):  
Operator Approach ◽  
Linear Spaces

Atomic Decompositions of Fuzzy Normed Linear Spaces for Wavelet Applications

Informatica ◽  
2014 ◽  
Vol 25 (4) ◽  
pp. 643-662 ◽  
Author(s):  
Sorin Nădăban ◽  
Ioan Dzitac
Keyword(s):  
Atomic Decompositions ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Wavelet Applications

Sub-normed Z-linear Spaces on Commutative Semi-group

2012 ◽  
Vol 14 (2) ◽  
pp. 157
Author(s):  
Yanqiu WANG ◽  
Huaxin ZHAO
Keyword(s):  
Semi Group ◽  
Linear Spaces

scholarly journals Spectral properties of some unions of linear spaces

2021 ◽  
pp. 108985
Author(s):  
Chun-Kit Lai ◽  
Bochen Liu ◽  
Hal Prince
Keyword(s):  
Spectral Properties ◽  
Linear Spaces

scholarly journals On a general bilinear functional equation

2021 ◽  
Author(s):  
Anna Bahyrycz ◽  
Justyna Sikorska
Keyword(s):  
Functional Equation ◽  
Linear Equation ◽  
General Linear ◽  
Linear Spaces ◽  
General Linear Equation ◽  
Bilinear Functional

AbstractLet X, Y be linear spaces over a field $${\mathbb {K}}$$ K . Assume that $$f :X^2\rightarrow Y$$ f : X 2 → Y satisfies the general linear equation with respect to the first and with respect to the second variables, that is, for all $$x,x_i,y,y_i \in X$$ x , x i , y , y i ∈ X and with $$a_i,\,b_i \in {\mathbb {K}}{\setminus } \{0\}$$ a i , b i ∈ K \ { 0 } , $$A_i,\,B_i \in {\mathbb {K}}$$ A i , B i ∈ K ($$i \in \{1,2\}$$ i ∈ { 1 , 2 } ). It is easy to see that such a function satisfies the functional equation for all $$x_i,y_i \in X$$ x i , y i ∈ X ($$i \in \{1,2\}$$ i ∈ { 1 , 2 } ), where $$C_1:=A_1B_1$$ C 1 : = A 1 B 1 , $$C_2:=A_1B_2$$ C 2 : = A 1 B 2 , $$C_3:=A_2B_1$$ C 3 : = A 2 B 1 , $$C_4:=A_2B_2$$ C 4 : = A 2 B 2 . We describe the form of solutions and study relations between $$(*)$$ ( ∗ ) and $$(**)$$ ( ∗ ∗ ) .

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