Results 131 to 140 of about 6,200 (156)
Some of the next articles are maybe not open access.
On the spectrum of the Laplacian
Mathematische Annalen, 2013Let \((M,g)\) be a complete non-compact Riemannian manifold. Let \(\Delta:=\delta d\) be the Laplacian acting on the space of smooth functions of compact support on \(M\); \(\Delta\) has a unique self-adjoint extension to \(L^2(M)\) which is densely defined and nonnegative.
Charalambous, N. +3 more
openaire +2 more sources
SPECTRUM OF THE LAPLACIAN OF COMPACT MANIFOLDS
Acta Mathematica Scientia, 1996The authors prove the following two results: 1. Let \(M\) be a compact, orientable embedded hypersurface of a compact orientable Riemannian manifold \(N\). Suppose that the Ricci curvature of \(N\) is bounded below by a positive number \(k\). Then \(\lambda_1>k/2\), where \(\lambda_1\) is the first Neumann eigenvalue of the Laplacian of \(M\). 2. Let \(
Xu, Senlin +3 more
openaire +2 more sources
On the Laplacian Szeged spectrum of paths
Iranian journal of mathemathical chemistry, 2020We present explicit formulas for the Laplacian Szeged eigenvalues of paths, grids, $C_4$-nanotubes and of Cartesian products of paths with some other simple graphs. A number of open problems is listed.
openaire +3 more sources
The spectrum of the -Laplacian with singular weight
Nonlinear Analysis: Theory, Methods & Applications, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Montenegro, Marcelo, Lorca, Sebastián
openaire +2 more sources
2010
This chapter gives a self-contained introduction into the Laplacian of compact Riemann surfaces. We prove the spectral theorem using the heat kernel which is given explicitly in Section 7.4 for the hyperbolic plane and in Section 7.5 for the compact quotients. As a tool we use the Abel transform which is introduced in Section 7.3.
openaire +1 more source
This chapter gives a self-contained introduction into the Laplacian of compact Riemann surfaces. We prove the spectral theorem using the heat kernel which is given explicitly in Section 7.4 for the hyperbolic plane and in Section 7.5 for the compact quotients. As a tool we use the Abel transform which is introduced in Section 7.3.
openaire +1 more source
The Laplacian Spectrum of a Graph
SIAM Journal on Matrix Analysis and Applications, 1990Let G be a graph. The Laplacian matrix $L(G) = D(G) - A(G)$ is the difference of the diagonal matrix of vertex degrees and the 0-1 adjacency matrix. Various aspects of the spectrum of $L(G)$ are investigated. Particular attention is given to multiplicities of integer eigenvalues and to the effect on the spectrum of various modifications of G.
Robert Grone +2 more
openaire +1 more source
On the Fu?�k Spectrum of the p-Laplacian
Nonlinear Differential Equations and Applications, 2004Let \(\Omega\) be a bounded domain in \({\mathbb R}^n\), \(n\geq1\).
openaire +1 more source
The spectrum of the Laplacian on fractals
2021In this work, we review some of the major results concerning dimension and spectral theory on self-affine and self-similar fractal sets. After a focused exposition on the underlying iterated function systems, measure theoretic results are used to determine the Hausdorff dimension of arbitrary self-similar sets.
openaire +1 more source
The Spectrum of the Laplacian on the Pentagasket
2003The spectrum of the fully symmetric Laplacian on the fractal pentagasket is studied by theoretical and experimental methods. We show how to construct derived eigenspaces of high multiplicity for both Dirichlet and Neumann spectrum starting from primitive Neumann eigenspaces.
Bryant Adams +3 more
openaire +1 more source
Spectrum of the Laplacian on a Domain Perturbed by Small Resonators
SIAM Journal on Mathematical Analysis, 2023Andrii Khrabustovskyi +1 more
exaly