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Special invariant operators I

Jarolím Bureš (1996)

Commentationes Mathematicae Universitatis Carolinae

The aim of the first part of a series of papers is to give a description of invariant differential operators on manifolds with an almost Hermitian symmetric structure of the type $G / B$ which are defined on bundles associated to the reducible but undecomposable representation of the parabolic subgroup $B$ of the Lie group $G$ . One example of an operator of this type is the Penrose’s local twistor transport. In this part general theory is presented, and conformally invariant operators are studied in more...

Spectra of Compact Locally Symmetric Manifolds of Negative Curvature.

J.J. Duistermaat, J.A.C. Kolk (1979)

Inventiones mathematicae

Spectra of manifolds with small handles.

I. Chavel, E.A. Feldman (1981)

Commentarii mathematici Helvetici

Spectral analysis of non-compact manifolds using commutator methods

P. D. Hislop (1987/1988)

Séminaire Équations aux dérivées partielles (Polytechnique)

Spectral analysis on singular spaces

Jochen Brüning (1989)

Journées équations aux dérivées partielles

Spectral and scattering theory for symbolic potentials of order zero

Andrew Hassell, Richard Melrose, András Vasy (2000/2001)

Séminaire Équations aux dérivées partielles

Spectral Asymmetrie and Zeta Functions.

Mariusz Wodzicki (1982)

Inventiones mathematicae

Spectral asymptotics for manifolds with cylindrical ends

Tanya Christiansen, Maciej Zworski (1995)

Annales de l'institut Fourier

The spectrum of the Laplacian on manifolds with cylindrical ends consists of continuous spectrum of locally finite multiplicity and embedded eigenvalues. We prove a Weyl-type asymptotic formula for the sum of the number of embedded eigenvalues and the scattering phase. In particular, we obtain the optimal upper bound on the number of embedded eigenvalues less than or equal to $r^{2}, 𝒪 (r^{n})$ , where $n$ is the dimension of the manifold.

Spectral asymptotics of Laplace operators on surfaces with cusps.

L.B. Parnovski (1995)

Mathematische Annalen

Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds.

Manlio Bordoni (1994)

Mathematische Annalen

Spectral geometry and scattering theory for certain complete surfaces of finite volume.

Werner Müller (1992)

Inventiones mathematicae

Spectral Geometry and the Kaehler Condition for Complex Manifolds.

Peter B. Gilkey (1974)

Inventiones mathematicae

Spectral Geometry for Certain Noncompact Riemannian Manifolds.

Harold Donnelly (1979)

Mathematische Zeitschrift

Spectral Geometry of Compact Hermitian Symmetric Submanifolds.

Seiichi Udagawa (1986)

Mathematische Zeitschrift

Spectral geometry of harmonic maps into warped product manifolds. II.

Yun, Gabjin (2001)

International Journal of Mathematics and Mathematical Sciences

Spectral geometry of semi-algebraic sets

Mikhael Gromov (1992)

Annales de l'institut Fourier

The spectrum of the Laplace operator on algebraic and semialgebraic subsets $A$ in $R^{N}$ is studied and the number of small eigenvalues is estimated by the degree of $A$ .

Spectral invariant of the zeta function of the Laplacian on $Sp (r + 1) / Sp (1) \times Sp (r)$

Neelacanta Sthanumoorthy (1991)

Archivum Mathematicum

Spectral isolation of bi-invariant metrics on compact Lie groups

Carolyn S. Gordon, Dorothee Schueth, Craig J. Sutton (2010)

Annales de l’institut Fourier

We show that a bi-invariant metric on a compact connected Lie group $G$ is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric $g_{0}$ on $G$ there is a positive integer $N$ such that, within a neighborhood of $g_{0}$ in the class of left-invariant metrics of at most the same volume, $g_{0}$ is uniquely determined by the first $N$ distinct non-zero eigenvalues of its Laplacian (ignoring multiplicities). In the case where $G$ is simple, $N$ can be chosen to be two....

Spectral resonances for the Laplace-Beltrami operator

Stephen De Bièvre, Peter D. Hislop (1988)

Annales de l'I.H.P. Physique théorique

Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger operator in two dimensions

László Erdős (2002)

Annales de l’institut Fourier

We show that the lowest eigenvalue of the magnetic Schrödinger operator on a line bundle over a compact Riemann surface $M$ is bounded by the $L^{1}$ -norm of the magnetic field $B$ . This implies a similar bound on the multiplicity of the ground state. An example shows that this degeneracy can indeed be comparable with $\int_{M} | B |$ even in case of the trivial bundle.

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