Quantitative self adjoint operator direct approximations

Volume 10, Issue 5, pp 2788--2797 http://dx.doi.org/10.22436/jnsa.010.05.45

Publication Date: May 25, 2017 Submission Date: July 09, 2016

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Authors

George A. Anastassiou - Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.

Abstract

Here we give a series of self adjoint operator positive linear operators general results. Then we present specific similar results related to neural networks. This is a quantitative treatment to determine the degree of self adjoint operator uniform approximation with rates, of sequences of self adjoint positive linear operators in general, and in particular of self adjoint specific neural network operators. The approach is direct relying on Gelfand’s isometry.

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Keywords

• Self adjoint operator
• Hilbert space
• positive linear operator
• Bernstein polynomials
• neural network operators.

MSC

•  41A17
•  41A25
•  41A36
•  41A80
•  47A58
•  47A60
•  47A67

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