Matris Formda Kompleks Değerli Kısmi Diferensiyel Denklemlerin Çözümleri Yardımıyla Kompleks Matris Değerli Fonksiyonlara Yaklaşım Üzerine

Year 2018, Volume: 22 Issue: 3, 1169 - 1174, 20.09.2018

Yeşim Sağlam Özkan , Sezayi Hızlıyel

https://doi.org/10.19113/sdufenbed.470192

Abstract

Bu çalışmada

$A =\alpha^{(0)}+\alpha ^{(1)}\phi +\alpha^{(2)}\overline{\phi}$,
$B =\beta ^{(0)}+\beta ^{(1)}\phi +\beta ^{(2)}\overline{\phi}$,

lineer katsayılara sahip olan

$ \frac{\partial w}{\partial \bar{\phi}}=Aw+B\overline{w}$   

denkleminin çözümleri araştırıldı. Bu çözümler kullanılarak $w=K^{(0)}+\phi K^{(1)} +\bar{\phi} K^{(2)}$ formuna sahip kompleks matris değerli fonksiyonlara yaklaşıldı. Burada $\phi$, $Q$-holomorf fonksiyonlar için bir doğurucu çözümdür.

Keywords

Genelleştirilmiş Beltrami sistemleri, Genelleştirilmiş Q-holomorf fonksiyonlar, Weierstrass-Stone yaklaşım teoremi

On the Approximation to Complex Matrix-valued Functions by Using Solutions of Partial Complex Differential Equation in Matrix Form

Abstract

In this work, we seek  the solutions of the equation  

$\frac{\partial w}{\partial \bar{\phi}}=Aw+B\overline{w}$

with linear coefficients

$A=\alpha^{(0)}+\alpha ^{(1)}\phi +\alpha^{(2)}\overline{\phi}$,
$B=\beta ^{(0)}+\beta ^{(1)}\phi +\beta ^{(2)}\overline{\phi}$,

such that using this solutions we approximated to complex matrix valued function which possess the form $w=K^{(0)}+\phi K^{(1)} +\bar{\phi} K^{(2)}$. Here $\phi$ is a generating solution for $Q$-holomorphic functions.

Keywords

Generalized Beltrami systems, Generalized Q-holomorphic functions, Weierstrass-Stone approximation

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