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December 2021 Inner-product quasilinear spaces with applications in signal processing
Yilmaz Yilmaz, Halise Levent
Adv. Studies: Euro-Tbilisi Math. J. 14(4): 125-146 (December 2021). DOI: 10.3251/asetmj/1932200818

Abstract

If certain characteristics of a non-deterministic signal are known, can some approximate results be obtained concerning the frequency, deterministic autocorrelation or other characteristics of the signal? The mathematical techniques we have developed allow us to obtain some approximate estimations of this type. In this way we use some new mathematical methods so called quasilinear functional analysis. Interval analysis also in the scope of this area and we use complex interval-valued signals in calculations. Especially, in this work, we give some special properties and results of inner-product quasilinear spaces which are generalizations of classical inner-product spaces. By this results we give easy examples of approximate estimations of deterministic autocorrelation of some semi non-deterministic signals or signals with inexact data. Further, we have constructed the space $\mathbb{I}l_{2}$ and we have showed that $\mathbb{I}l_{2}$ is an inner-product quasilinear space. This space provides a basis for an estimation of deterministic autocorrelation of the signals with inexact data.

Citation

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Yilmaz Yilmaz. Halise Levent. "Inner-product quasilinear spaces with applications in signal processing." Adv. Studies: Euro-Tbilisi Math. J. 14 (4) 125 - 146, December 2021. https://doi.org/10.3251/asetmj/1932200818

Information

Received: 14 November 2020; Accepted: 25 June 2021; Published: December 2021
First available in Project Euclid: 16 December 2021

Digital Object Identifier: 10.3251/asetmj/1932200818

Subjects:
Primary: 32A70
Secondary: 47H04 , ‎54C60‎ , 60B15 , 65G40

Keywords: complex interval-valued signals , eterministic autocorrelation , Hilbert quasilinear spaces , inner-product quasilinear spaces , non-deterministic signals

Rights: Copyright © 2021 Tbilisi Centre for Mathematical Sciences

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Vol.14 • No. 4 • December 2021
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