scholarly journals On some classes of almost periodic functions in abstract spaces

2004 ◽  
Vol 2004 (61) ◽  
pp. 3237-3247 ◽  
Author(s):  
Dariusz Bugajewski ◽  
Gaston M. N'Guérékata
Keyword(s):  
Banach Space ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Superposition Operator ◽  
Periodic Functions ◽  
Partial Differential ◽  
Abstract Spaces

We deal withC(n)-almost periodic functions taking values in a Banach space. We give several properties of such functions, in particular, we investigate their behavior in view of differentiation as well as integration. The superposition operator acting in the space of such functions is also under consideration. Some applications to ordinary as well as partial differential equations are presented. Moreover, we introduce the class of the so-called asymptoticallyC(n)-almost periodic functions and give some of their properties.

scholarly journals A Note on the Topological Group c0

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 77
Author(s):  
Michael Megrelishvili
Keyword(s):  
Banach Space ◽  
Topological Group ◽  
Unit Sphere ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Semigroup Compactification ◽  
Weakly Almost Periodic ◽  
Open Question

A well-known result of Ferri and Galindo asserts that the topological group c 0 is not reflexively representable and the algebra WAP ( c 0 ) of weakly almost periodic functions does not separate points and closed subsets. However, it is unknown if the same remains true for a larger important algebra Tame ( c 0 ) of tame functions. Respectively, it is an open question if c 0 is representable on a Rosenthal Banach space. In the present work we show that Tame ( c 0 ) is small in a sense that the unit sphere S and 2 S cannot be separated by a tame function f ∈ Tame ( c 0 ) . As an application we show that the Gromov’s compactification of c 0 is not a semigroup compactification. We discuss some questions.

scholarly journals Rhythm Drivers, Physical Properties, Mechanisms of Formation

2021 ◽  
Vol 248 ◽  
pp. 01007
Author(s):  
Mikhail Mazurov
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Nonlinear System ◽  
Differential Equations ◽  
Physical Properties ◽  
Ordinary Differential Equations ◽  
Numerical Study ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Mechanisms Of Formation

A mathematical model of the pacemaker is presented in the form of a nonlinear system of ordinary differential equations and in the form of a system of partial differential equations for distributed pacemakers. For the numerical study of the properties of the pacemaker, a modified axiomatic Wiener-Rosenbluth method was used using the properties of uniform almost periodic functions. Physical foundations, mechanisms of formation, properties of point and distributed pacemakers are described in detail.

scholarly journals Notes on almost-periodicity in topological vector spaces

1986 ◽  
Vol 9 (1) ◽  
pp. 201-204 ◽  
Author(s):  
Gaston Mandata N'guérékata
Keyword(s):  
Differential Equations ◽  
Almost Periodic Functions ◽  
Vector Spaces ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Topological Vector Spaces ◽  
Abstract Differential Equations

A study is made of almost-periodic functions in topological vector spaces with applications to abstract differential equations.

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