Estimates for Sums of Eigenvalues of the Laplacian
โ Scribed by P. Kroger
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 310 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract Let ฮป~__k__~(__G__) be the __k__th Laplacian eigenvalue of a graph __G__. It is shown that a tree __T__ with __n__ vertices has $\lambda\_{k}(T)\le \lceil { {n}\over{k}}\rceil$ and that equality holds if and only if __k__ < __n__, __k__|__n__ and __T__ is spanned by __k__ vertex disjoin
Po lya and G. Szego showed in 1951 that for simply connected plane domains, the first eigenvalue of the Laplacian (with Dirichlet boundary conditions) is maximal for a disk, under a conformal mapping normalization. That is, if f (z) is a conformal map of a disk D onto a bounded, simply connected pla
## Abstract It is shown that there exist domains ฮฉ โ โ^__N__^, which outside of some ball coincide with the strip โ^__N__ โ 1^ ร (0, ฯ) and for which the Dirichlet Laplacian โ ฮ has eigenvalues within the subinterval (1, 4) of the essential spectrum (1, โ).