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Some Results on the Laplacian Spectrum
Computers and Mathematics With Applications, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Muhuo Liu, Bolian Liu
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The Laplacian Spectrum of a Graph II
SIAM Journal on Discrete Mathematics, 1994Summary: [For Part I see \textit{R. Grone}, \textit{R. Merris} and \textit{V. S. Sunder}, SIAM J. Matrix Anal. Appl. 11, No. 2, 218-238 (1990; Zbl 0733.05060).] Let \(G\) be a graph. Denote by \(D(G)\) the diagonal matrix of its vertex degrees and by \(A(G)\) its adjacency matrix. Then \(L(G) = D(G) -A(G)\) is the Laplacian matrix of \(G\).
Russell Merris, Robert Gröne
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On the Essential Spectrum of the Laplacian and the Drifted Laplacian
Journal of Functional Analysis, 2014 This paper concerns the $L^2$ essential spectrum of the Laplacian $Δ$ and the drift Laplacian $Δ_f$ on complete Riemannian manifolds endowed with a weighted measure $e^{-f}d\;vol_g$. We prove that the essential spectrum of the drift Laplacian $Δ_f$ is $[0,+\infty) $ provided the Bakry-Émery curvature tensor $Ric_f$ is nonnegative and $f$ has sublinear ...
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The Spectrum and Laplacian Spectrum of the Dice Lattice
Journal of Statistical Physics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Shuli, Yan, Weigen, Tian, Tao
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Laplacian Controllability for Graphs with Integral Laplacian Spectrum
Mediterranean Journal of Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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
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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
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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.
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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
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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.
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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.
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