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Effets de bord pour un tambour à bord fractal

Jean Brossard (1984/1985)

Séminaire de théorie spectrale et géométrie

Eigenmodes of the damped wave equation and small hyperbolic subsets

Gabriel Rivière (2014)

Annales de l’institut Fourier

We study stationary solutions of the damped wave equation on a compact and smooth Riemannian manifold without boundary. In the high frequency limit, we prove that a sequence of $β$ -damped stationary solutions cannot be completely concentrated in small neighborhoods of a small fixed hyperbolic subset made of $β$ -damped trajectories of the geodesic flow.The article also includes an appendix (by S. Nonnenmacher and the author) where we establish the existence of an inverse logarithmic strip without eigenvalues...

Eigenvalue asymptotics for Neumann Laplacian in domains with ultra-thin cusps

Victor Ivrii (1998/1999)

Séminaire Équations aux dérivées partielles

Asymptotics with sharp remainder estimates are recovered for number $N (τ)$ of eigenvalues of the generalized Maxwell problem and for related Laplacians which are similar to Neumann Laplacian. We consider domains with ultra-thin cusps (with $exp (- | x |^{m + 1}$ ) width ; $m > 0$ ) and recover eigenvalue asymptotics with sharp remainder estimates.

Eigenvalue asymptotics for randomly perturbed non-self adjoint operators

Mildred Hager (2007)

Journées Équations aux dérivées partielles

Eigenvalue asymptotics for Schrödinger and Dirac operators with the constant magnetic field and with electric potential decreasing at infinity

Victor Ivrii (1991)

Journées équations aux dérivées partielles

Eigenvalue asymptotics for the Dirac operator in strong constant magnetic fields.

Raikov, G.D. (1999)

Mathematical Physics Electronic Journal [electronic only]

Eigenvalue asymptotics for the Pauli operator in strong nonconstant magnetic fields

Georgi D. Raikov (1999)

Annales de l'institut Fourier

We consider the Pauli operator $H (μ) : = {(\sum_{j = 1}^{m} σ_{j} (- i \frac{\partial}{\partial x_{j}} - μ A_{j}))}^{2} + V$ selfadjoint in $L^{2} (ℝ^{m}; ℂ^{2})$ , $m = 2, 3$ . Here $σ_{j}$ , $j = 1, ..., m$ , are the Pauli matrices, $A : = (A_{1}, ..., A_{m})$ is the magnetic potential, $μ > 0$ is the coupling constant, and $V$ is the electric potential which decays at infinity. We suppose that the magnetic field generated by $A$ satisfies some regularity conditions; in particular, its norm is lower-bounded by a positive constant, and, in the case $m = 3$ , its direction is constant. We investigate the asymptotic behaviour as $μ \to \infty$ of the number of the eigenvalues of $H (μ)$ smaller than...

Eigenvalue asymptotics for the Schrödinger operator with perturbed periodic potential.

G.D. Raikov (1992)

Inventiones mathematicae

Eigenvalue clusters of the Landau Hamiltonian in the exterior of a compact domain.

Pushnitski, Alexander, Rozenblum, Grigori (2007)

Documenta Mathematica

Eigenvalue distribution of random operators and matrices

Leonid Pastur (1991/1992)

Séminaire Bourbaki

Eigenvalue distributions of some degenerate elliptic operators: an approach via entropy numbers.

D.E. Edmunds, H. Triebel (1994)

Mathematische Annalen

Eigenvalue estimates for a class of operators related to self-similar measures

Michael Solomyak (1994)

Journées équations aux dérivées partielles

Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics

Michael Hitrik, Karel Pravda-Starov (2013)

Annales de l’institut Fourier

For a class of non-selfadjoint $h$ –pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin. Specifically, assuming that the quadratic approximations of the principal symbol of the operator along the double characteristics enjoy a partial ellipticity property along a suitable subspace of the phase space, namely their singular space, we give a precise description of...

Eigenvalues of the negative Laplacian for arbitrary multiply connected domains.

Zayed, E.M.E. (1996)

International Journal of Mathematics and Mathematical Sciences

Équirépartition de fonctions propres pour des problèmes aux limites

Patrick Gérard, Éric Leichtnam (1992)

Journées équations aux dérivées partielles

Error estimate in the generalized Szegö theorem

Ari Laptev, Yu Safarov (1991)

Journées équations aux dérivées partielles

Estimates for second order derivatives of eigenvectors in thin anisotropic plates with variable thickness.

Nazarov, S.A. (2004)

Journal of Mathematical Sciences (New York)

Estimates on the number of scattering poles near the real axis for strictly convex obstacles

Johannes Sjöstrand, Maciej Zworski (1993)

Annales de l'institut Fourier

For the Dirichlet Laplacian in the exterior of a strictly convex obstacle, we show that the number of scattering poles of modulus $\leq r$ in a small angle $θ$ near the real axis, can be estimated by Const $θ^{3 / 2} r^{n}$ for $r$ sufficiently large depending on $θ$ . Here $n$ is the dimension.

Estimation des valeurs propres d'opérateurs elliptiques sur des ouverts non bornés

Jacqueline Fleckinger (1980)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Estimation du reste dans la théorie spectrale d'une classe de problèmes d'opérateur elliptiques dégénérés

Pham The Lai (1975)

Journées équations aux dérivées partielles

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