Eigenvalues of the normalized complex Laplacian for finite electrical networks
Abstract:
The spectrum of the normalized complex Laplacian for electrical networks is analyzed. We show that eigenvalues lie in a larger region compared to the case of the real Laplacian. We show the existence of eigenvalues with negative real part and absolute value greater than $2$. An estimate from below for the first non-vanishing eigenvalue in modulus is provided. We supplement the estimates with examples, showing sharpness.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsmonat/-jahr | 03.2021 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X KITopen-ID: 1000130241 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 15 S. |
| Serie | CRC 1173 Preprint ; 2021/10 |
| Projektinformation | SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019) |
| Externe Relationen | Siehe auch |
| Schlagwörter | finite weighted graphs, complex Laplacian, electrical networks, spectral estimates |