scholarly journals Closure of the linear span of an exponential system in a weighted Banach space

2017 ◽  
pp. 131-146
Author(s):  
Elias Zikkos
Keyword(s):  
Banach Space ◽  
Linear Span ◽  
Exponential System ◽  
Weighted Banach Space

scholarly journals EXPONENTIAL POLYNOMIAL APPROXIMATION OF WEIGHTED BANACH SPACE ON ℝn

2012 ◽  
Vol 55 (1) ◽  
pp. 115-121 ◽  
Author(s):  
XIANGDONG YANG
Keyword(s):  
Banach Space ◽  
Polynomial Approximation ◽  
Sufficient Conditions ◽  
Uniform Norm ◽  
Continuous Functions ◽  
Necessary And Sufficient Conditions ◽  
Exponential Polynomial ◽  
Exponential System ◽  
Weighted Banach Space ◽  
Necessary And Sufficient

AbstractNecessary and sufficient conditions for the incompleteness of exponential system in Cα are characterised, where Cα is the weighted Banach space of complex continuous functions f defined on ℝn with f(t)exp(−α(t)) vanishing at infinity in the uniform norm.

scholarly journals Some results on the span of families of Banach valued independent, random variables

1991 ◽  
Vol 14 (2) ◽  
pp. 381-384
Author(s):  
Rohan Hemasinha
Keyword(s):  
Banach Space ◽  
Probability Space ◽  
Linear Span ◽  
Random Variables ◽  
Isomorphic Copy ◽  
Independent Random Variables ◽  
Closed Linear Span

LetEbe a Banach space, and let(Ω,ℱ,P)be a probability space. IfL1(Ω)contains an isomorphic copy ofL1[0,1]then inLEP(Ω)(1≤P<∞), the closed linear span of every sequence of independent,Evalued mean zero random variables has infinite codimension. IfEis reflexive orB-convex and1<P<∞then the closed(in LEP(Ω))linear span of any family of independent,Evalued, mean zero random variables is super-reflexive.

scholarly journals On Weighted Polynomial Approximation With Gaps

2005 ◽  
Vol 178 ◽  
pp. 55-61 ◽  
Author(s):  
Guantie Deng
Keyword(s):  
Banach Space ◽  
Continuous Function ◽  
Polynomial Approximation ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Weighted Polynomial Approximation ◽  
Necessary And Sufficient Condition ◽  
Weighted Banach Space ◽  
Nonnegative Continuous Function ◽  
Necessary And Sufficient

Let α be a nonnegative continuous function on ℝ. In this paper, the author obtains a necessary and sufficient condition for polynomials with gaps to be dense in Cα, where Cα is the weighted Banach space of complex continuous functions ƒ on ℝ with ƒ(t) exp(−α(t)) vanishing at infinity.

Minimality and Closeure of Random Exponential Systems

2011 ◽  
Vol 130-134 ◽  
pp. 188-190
Author(s):  
Feng Yan ◽  
Xiao Ling Liu ◽  
Su Mei Zhang
Keyword(s):  
Banach Space ◽  
Entire Function ◽  
Dirichlet Series ◽  
Uniform Norm ◽  
Continuous Functions ◽  
Weighted Banach Space

In this paper, we study the minimality properties of random exponential systems in , where is a weighted Banach space of complex continuous functions of on with vanishing at infinity, in the uniform norm with respect to the weight . We prove that, if is incomplete in , then is minimal and each function in can be extended to an entire function respresented by a Dirichlet series.

ANTI-PERIODIC TYPE BOUNDARY VALUE PROBLEMS FOR SINGULAR MULTI-TERM FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS

2013 ◽  
Vol 24 (06) ◽  
pp. 1350047 ◽  
Author(s):  
YUJI LIU
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Continuous Operator ◽  
Weighted Banach Space ◽  
Fractional Differential ◽  
The Fixed Point Theorem ◽  
Type Boundary

Results on the existence of solutions of anti-periodic type boundary value problems for singular multi-term fractional differential equations with impulse effects are established. We first transform the problem into a hybrid system, then construct a weighted Banach space and a completely continuous operator, and finally, we use the fixed point theorem in the Banach space to prove the main results. An example is given to illustrate the efficiency of the main theorems.

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