On the differentiability of parametrized families of linear operators and the sensitivity of their stationary vectors
type: Item
instance of: scholarly article
title: On the differentiability of parametrized families of linear operators and the sensitivity of their stationary vectors
zbMATH Open document ID: 1219.47027
author: Heinz Weisshaupt
published in: Periodica Mathematica Hungarica
publication date: 2011-02-08T00:00:00Z
review text: In this article, the differentiability of functions of stationary vectors associated to operator-valued functions as well as the differentiability of the operator-valued functions themselves is studied. In particular, it is shown that the derivative of a weakly differentiable parametric family of continuous operators is again a parametric family of continuous operators. This result is then applied to kernel operators. Further, the sensitivity of continuous linear operators and the sensitivity of their stationary vectors is investigated.
reviewed by: Birgit Jacob
Mathematics Subject Classification ID: 47A56
Mathematics Subject Classification ID: 28A15
Mathematics Subject Classification ID: 47N30
zbMATH DE Number: 5848591
zbMATH Keywords: differentiation
zbMATH Keywords: operator-valued functions
zbMATH Keywords: stationary vectors
zbMATH Keywords: stationary distributions
zbMATH Keywords: differentiation of operators
zbMATH Keywords: differentiation of Markov kernels
zbMATH Keywords: measure-valued differentiation
MaRDI profile type: Publication
full work available at URL: s10998-009-0147-2
OpenAlex ID: W2023258952
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DOI: 10.1007/S10998-009-0147-2
description: scientific article; zbMATH DE number 5848591