Abstract
In this paper, a boundary version of the Schwarz lemma has been considered for driving point impedance functions at s=0 point of the imaginary axis. Accordingly, under Z(0)=0condition, the modulus of the derivative of the Z(s) function has been considered from below. Here, Z(alfa), c1 and c2 coefficients of the Taylor expansion of the Z(s)=beta+c1(s-alfa)+... function have been used in the obtained inequalities. The sharpness of these inequalities has also been proved.
References
- Sharma A., Soni, T. 2017. A Review on Passive Network Synthesis Using Cauer Form, World Journal of Wireless Devices and Engineering, 1 (1): 39–46.
- Bakshi M., Sule V., Baghini M. S. 2016. Stabilization Theory for Active Multi Port Networks, arXiv preprint (aXiv:1606.03194).
- Reza F. 1962. A Bound for the Derivative of Positive Real Functions, SIAM Review, 4 (1): 40–42.
- Richards P. I. 1947. A Special Class of Functions with Positive Real Part in a Half-Plane. Duke Mathematical Journal 1947, 14 (3): 777–786. DOI: 10.1215/S0012-7094-47-01461-0.
- Osserman R. 2000. A Sharp Schwarz Inequality on the Boundary. Proceedings of the American Mathematical Society, 128 (12): 3513–3517.
- Dubinin V. 2004. The Schwarz Inequality on the Boundary for Functions Regular in the Disk, Journal of Mathematical Sciences, 122 (6): 3623–3629.
- Azeroğlu T. A., Örnek B. N. (2013). A Refined Schwarz Inequality on the Boundary, Complex Variables and Elliptic Equations, 58 (4): 571–577.
- Örnek B. N. 2013. Sharpened Forms of the Schwarz Lemma on the Boundary, Bulletin of the Korean Mathematical Society, 50 (6): 2053–2059.
Abstract
Bu çalışmada, Schwarz lemmasının bir sınır versiyonu,
süren nokta empedans fonksiyonları için sanal eksen üzerindeki s=0 noktasında
değerlendirilmiştir. Buna göre, Z(0)=0 koşulu altında, Z(s) fonksiyonunun
türevinin modülü aşağıdan değerlendirilmiştir. Burada, elde edilen
eşitsizliklerde, Z(s)=beta+c1(s-alfa)+.... fonksiyonunun Taylor
açılımındaki , Z(alfa), c1 ve c2 katsayıları
kullanılmıştır. Aynı zamanda, bu eşitsizliklerin keskinliği ispatlanmıştır.
References
- Sharma A., Soni, T. 2017. A Review on Passive Network Synthesis Using Cauer Form, World Journal of Wireless Devices and Engineering, 1 (1): 39–46.
- Bakshi M., Sule V., Baghini M. S. 2016. Stabilization Theory for Active Multi Port Networks, arXiv preprint (aXiv:1606.03194).
- Reza F. 1962. A Bound for the Derivative of Positive Real Functions, SIAM Review, 4 (1): 40–42.
- Richards P. I. 1947. A Special Class of Functions with Positive Real Part in a Half-Plane. Duke Mathematical Journal 1947, 14 (3): 777–786. DOI: 10.1215/S0012-7094-47-01461-0.
- Osserman R. 2000. A Sharp Schwarz Inequality on the Boundary. Proceedings of the American Mathematical Society, 128 (12): 3513–3517.
- Dubinin V. 2004. The Schwarz Inequality on the Boundary for Functions Regular in the Disk, Journal of Mathematical Sciences, 122 (6): 3623–3629.
- Azeroğlu T. A., Örnek B. N. (2013). A Refined Schwarz Inequality on the Boundary, Complex Variables and Elliptic Equations, 58 (4): 571–577.
- Örnek B. N. 2013. Sharpened Forms of the Schwarz Lemma on the Boundary, Bulletin of the Korean Mathematical Society, 50 (6): 2053–2059.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Submission Date | December 5, 2018 |
| Acceptance Date | May 20, 2019 |
| Publication Date | June 28, 2019 |
| DOI | https://doi.org/10.17798/bitlisfen.492656 |
| IZ | https://izlik.org/JA97US94ZT |
| Published in Issue | Year 2019 Volume: 8 Issue: 2 |