In this post we will study integration in abstract spaces. Let \(E\) be a normed linear space and \(K\) the closed interval \([a,\,b]\) of the real number line. We consider an operator \(x = x(t),\) which need not be linear and maps \(K\) into \(E.\) In the following, we will call such an operator an abstract function on the interval \([a,\,b].\) For these functions, …
Category:
Functional Analysis
In this post we will study differentiation in abstract spaces. Definition of Derivatives Let \(E\) be a normed linear space and \(K\) the closed interval \([0,\,1]\) of the real number line. We consider an operator \(x = x(t),\) which need not be linear and maps \(K\) into \(E.\) In the following, we will call such an operator an abstract function on the interval \([0,\,1].\) …