Spectral asymptotics for nonlinear multiparameter problems with indefinite nonlinearities
Spectral asymptotics of Laplace operators on surfaces with cusps.
Spectral distances: results for Moyal plane and noncommutative torus.
Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds.
Spectral gap lower bound for the one-dimensional fractional Schrödinger operator in the interval
We prove a uniform lower bound for the difference λ₂ - λ₁ between the first two eigenvalues of the fractional Schrödinger operator , α ∈ (1,2), with a symmetric single-well potential V in a bounded interval (a,b), which is related to the Feynman-Kac semigroup of the symmetric α-stable process killed upon leaving (a,b). “Uniform” means that the positive constant appearing in our estimate is independent of the potential V. In the general case of α ∈ (0,2), we also find a uniform lower bound for...
Spectral geometry and scattering theory for certain complete surfaces of finite volume.
Spectral Geometry and the Kaehler Condition for Complex Manifolds.
Spectral Geometry for Certain Noncompact Riemannian Manifolds.
Spectral Geometry of Compact Hermitian Symmetric Submanifolds.
Spectral geometry of harmonic maps into warped product manifolds. II.
Spectral geometry of semi-algebraic sets
The spectrum of the Laplace operator on algebraic and semialgebraic subsets in is studied and the number of small eigenvalues is estimated by the degree of .
Spectral invariant of the zeta function of the Laplacian on
Spectral isolation of bi-invariant metrics on compact Lie groups
We show that a bi-invariant metric on a compact connected Lie group is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric on there is a positive integer such that, within a neighborhood of in the class of left-invariant metrics of at most the same volume, is uniquely determined by the first distinct non-zero eigenvalues of its Laplacian (ignoring multiplicities). In the case where is simple, can be chosen to be two....
Spectral properties of the adjoint operator and applications.
Spectral resonances for the Laplace-Beltrami operator
Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions
We show that the lowest eigenvalue of the magnetic Schrödinger operator on a line bundle over a compact Riemann surface is bounded by the -norm of the magnetic field . This implies a similar bound on the multiplicity of the ground state. An example shows that this degeneracy can indeed be comparable with even in case of the trivial bundle.
Spectral theory of invariant operators, sharp inequalities, and representation theory
The paper represents the lectures given by the author at the 16th Winter School on Geometry and Physics, Srni, Czech Republic, January 13-20, 1996. He develops in an elegant manner the theory of conformal covariants and the theory of functional determinant which is canonically associated to an elliptic operator on a compact pseudo-Riemannian manifold. The presentation is excellently realized with a lot of details, examples and open problems.
Spectral theory of translation surfaces : A short introduction
We define translation surfaces and, on these, the Laplace operator that is associated with the Euclidean (singular) metric. This Laplace operator is not essentially self-adjoint and we recall how self-adjoint extensions are chosen. There are essentially two geometrical self-adjoint extensions and we show that they actually share the same spectrum
Spectre asymptotique du revêtement universel des tores
Spectre conforme et métriques extrémales