About the mathematical expression of the observation operators

Eufrosina Otlacan (Romanian University Foundation of Science and Arts, G. Cristea (FURSA), Bucharest, Romania)

Kybernetes

ISSN: 0368-492X

Publication date: 1 December 2000

Abstract

The paper accepts the “functional paradigm” in the formative process of the image of an object. It holds that the used formulae must be mathematically demonstrated. As for many systems with memory, the frequently met formula is a defined integral. Its inferior limit is considered “the initial instant”. In this paper we show that: (1) The integral representation formula, that gives the image η (t) as a functional on the history ξ =ξ (τ),τ≤q t, of the evolutions both of the observed object and the observer, is only an approximate one. There exists the possibility to appreciate the order of size of the error. (2) The inferior limit of the integral may be mathematically determined and its choice requires some discussions. (3) A more precise formula of η (t) contains also a double integral upon a quadratic form of ξ(τ). The mathematical model is based on the differential calculus on the linear topological locally convex spaces.

Keywords

Citation

Otlacan, E. (2000), "About the mathematical expression of the observation operators", Kybernetes, Vol. 29 No. 9/10, pp. 1058-1068. https://doi.org/10.1108/03684920010342125

Download as .RIS

Publisher

:

MCB UP Ltd

Copyright © 2000, MCB UP Limited

Please note you might not have access to this content

You may be able to access this content by login via Shibboleth, Open Athens or with your Emerald account.
If you would like to contact us about accessing this content, click the button and fill out the form.
To rent this content from Deepdyve, please click the button.