Variational formulas and approximation theorems for the first eigenvalue in dimension one

DOI10.1007/BF02881877zbMath1012.34078OpenAlexW1521480444MaRDI QIDQ1609653

Chen Mu-Fa

Publication date: 15 August 2002

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02881877

zbMATH Keywords

both-sided estimateselliptic linear differential/difference operatorsfirst Dirichlet/Neumann eigenvaluesthe lowest eigenvalue

Mathematics Subject Classification ID

Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Linear boundary value problems for ordinary differential equations (34B05) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (24)

On the spectral gap of Boltzmann measures on the unit sphere ⋮ Approximation theorem for principle eigenvalue of discrete \(p\)-Laplacian ⋮ Spectral gap and convex concentration inequalities for birth-death processes ⋮ The first Dirichlet eigenvalue of birth-death process on trees ⋮ Efficient initials for computing maximal eigenpair ⋮ Mixed principal eigenvalues in dimension one ⋮ Speed of stability for birth-death processes ⋮ Extremal eigenvalues of measure differential equations with fixed variation ⋮ Lipschitzian norms and functional inequalities for birth-death processes ⋮ General estimate of the first eigenvalue on manifolds ⋮ A note on one-dimensional Poincaré inequalities by Stein-type integration ⋮ Variational formulas of Poincaré-type inequalities for birth-death processes. ⋮ Continuity in weak topology: higher order linear systems of ODE ⋮ Spectral gap and logarithmic Sobolev constant for continuous spin systems ⋮ On eigenfunctions of Markov processes on trees ⋮ Mixed eigenvalues of discrete \(p\)-Laplacian ⋮ New point view of spectral gap in functional spaces for birth-death processes ⋮ On the speed of convergence to stationarity of the Erlang loss system ⋮ Linear approximation of the first eigenvalue on compact manifolds ⋮ Computable Bounds for the Decay Parameter of a Birth–Death Process ⋮ Spectral gap of Boltzmann measures on unit circle ⋮ Extremal values of smallest eigenvalues of Hill's operators with potentials in \(L^1\) balls ⋮ A LOWER BOUND OF THE FIRST DIRICHLET EIGENVALUE OF A COMPACT MANIFOLD WITH POSITIVE RICCI CURVATURE ⋮ Representations for the extreme zeros of orthogonal polynomials

Cites Work

• Unnamed Item
• General formula for lower bound of the first eigenvalue on Riemannian manifolds
• Coupling, spectral gap and related topics. I
• Explicit bounds of the first eigenvalue.
• Analytic proof of dual variational formula for the first eigenvalue in dimension one
• Estimation of spectral gap for elliptic operators
• Estimation of spectral gap for Markov chains

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