Here $\phi$ is a generating solution for $Q$-holomorphic functions.
📌 3 Key Takeaways
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Objective & Hypothesis: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 $w=K^{(0)}+\phi K^{(1)} +\bar{\phi} K^{(2)}$.
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Key Findings & Data: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 $w=K^{(0)}+\phi K^{(1)} +\bar{\phi} K^{(2)}$.
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Conclusion & Impact:Here $\phi$ is a generating solution for $Q$-holomorphic functions.
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.
Özet
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.
ÖZKAN, Y. S., HIZLIYEL, S. (2018). On the Approximation to Complex Matrix-valued Functions by Using Solutions of Partial Complex Differential Equation in Matrix Form. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 22 - Sayı: 3, 1169–1174. https://ajindex.com/articles/309824
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