Regular Functions on Certain Infinite-dimensional Groups

1983 ◽  
pp. 141-166 ◽  
Author(s):  
Victor G. Kac ◽  
Dale H. Peterson
Keyword(s):  
Infinite Dimensional ◽  
Regular Functions

scholarly journals On an infinite-dimensional differential equation in vector distribution with discontinuous regular functions in a right hand side

1996 ◽  
Vol 9 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Michael V. Basin
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Unbounded Operator ◽  
Infinite Dimensional ◽  
Regular Functions ◽  
Right Hand ◽  
Equivalent Equation ◽  
Vector Distribution ◽  
Existence Conditions ◽  
Necessary And Sufficient

An infinite-dimensional differential equation in vector distribution in a Hilbert space is studied in case of an unbounded operator and discontinuous regular functions in a right-hand side. A unique solution (vibrosolution) is defined for such an equation, and the necessary and sufficient existence conditions for a vibrosolution are proved. An equivalent equation with a measure, which enables us to directly compute jumps of a vibrosolution at discontinuity points of a distribution function, is also obtained. The application of the obtained results to control theory is discussed in the conclusion.

Infinite Dimensional Analysis

1994 ◽  
Author(s):  
Charalambos D. Aliprantis ◽  
Kim C. Border
Keyword(s):  
Dimensional Analysis ◽  
Infinite Dimensional ◽  
Infinite Dimensional Analysis

Criterion of cyclically compactness infinite-dimensional normed module

2018 ◽  
Vol 2018 (3) ◽  
pp. 51-62
Author(s):  
V.I. Chilin ◽  
J.A. Karimov
Keyword(s):  
Infinite Dimensional ◽  
Normed Module
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