On the number of Courant-sharp Dirichlet eigenvalues

On Absorption times and Dirichlet Eigenvalues

This paper gives a stochastic representation in spectral terms for the absorption time T of a finite Markov chain which is irreducible and reversible outside the absorbing point. This yields quantitative informations on the parameters of a similar representation due to O’Cinneide for general chains admitting real eigenvalues. In the discrete time setting, if the underlying Dirichlet eigenvalues...

On the average number of sharp crossings of certain Gaussian random polynomials

Boundary Quasi-Orthogonality and Sharp Inclusion Bounds for Large Dirichlet Eigenvalues

We study eigenfunctions φj and eigenvalues Ej of the Dirichlet Laplacian on a bounded domain Ω ⊂ Rn with piecewise smooth boundary. We bound the distance between an arbitrary parameter E > 0 and the spectrum {Ej} in terms of the boundary L2-norm of a normalized trial solution u of the Helmholtz equation (∆ + E)u = 0. We also bound the L2-norm of the error of this trial solution from an eigenfun...

survey on the rule of the due & hindering relying on the sheikh ansaris ideas

قاعده مقتضی و مانع در متون فقهی کم و بیش مستند احکام قرار گرفته و مورد مناقشه فقهاء و اصولیین می باشد و مشهور معتقند مقتضی و مانع، قاعده نیست بلکه یکی از مسائل ذیل استصحاب است لذا نگارنده بر آن شد تا پیرامون این قاعده پژوهش جامعی انجام دهد. به عقیده ما مقتضی دارای حیثیت مستقلی است و هر گاه می گوییم مقتضی احراز شد یعنی با ماهیت مستقل خودش محرز گشته و قطعا اقتضاء خود را خواهد داشت مانند نکاح که ...

Sharp semiclassical estimates for the number of eigenvalues below a degenerate critical level

Abstract: We consider the semiclassical asymptotic behaviour of the number of eigenvalues smaller than E for elliptic operators in L(IR). We describe a method of obtaining remainder estimates related to the volume of the region of the phase space in which the principal symbol takes values belonging to the intervals [E; E + h], where E is close to E. This method allows us to derive sharp remaind...