Inverse spectral results on even dimensional tori

Carolyn S. Gordon; Pierre Guerini; Thomas Kappeler; David L. Webb

Displaying similar documents to “Inverse spectral results on even dimensional tori”

Conformally invariant trilinear forms on the sphere

Jean-Louis Clerc, Bent Ørsted (2011)

Annales de l’institut Fourier

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To each complex number $λ$ is associated a representation $π_{λ}$ of the conformal group $S O_{0} (1, n)$ on $𝒞^{\infty} (S^{n - 1})$ (spherical principal series). For three values $λ_{1}, λ_{2}, λ_{3}$ , we construct a trilinear form on $𝒞^{\infty} (S^{n - 1}) \times 𝒞^{\infty} (S^{n - 1}) \times 𝒞^{\infty} (S^{n - 1})$ , which is invariant by $π_{λ_{1}} \otimes π_{λ_{2}} \otimes π_{λ_{3}}$ . The trilinear form, first defined for $(λ_{1}, λ_{2}, λ_{3})$ in an open set of $ℂ^{3}$ is extended meromorphically, with simple poles located in an explicit family of hyperplanes. For generic values of the parameters, we prove uniqueness of trilinear invariant forms.

Normalization of bundle holomorphic contractions and applications to dynamics

François Berteloot, Christophe Dupont, Laura Molino (2008)

Annales de l’institut Fourier

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We establish a Poincaré-Dulac theorem for sequences ${(G_{n})}_{n \in ℤ}$ of holomorphic contractions whose differentials $d_{0} G_{n}$ split regularly. The resonant relations determining the normal forms hold on the moduli of the exponential rates of contraction. Our results are actually stated in the framework of bundle maps. Such sequences of holomorphic contractions appear naturally as iterated inverse branches of endomorphisms of $ℂ ℙ^{k}$ . In this context, our normalization result allows to estimate precisely...

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

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Let $A, B$ denote generic binary forms, and let $𝔲_{r} = {(A, B)}_{r}$ denote their $r$ -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the ${𝔲_{r}}$ . As a consequence, we show that each of the higher transvectants ${𝔲_{r} : r \geq 2}$ is redundant in the sense that it can be completely recovered from $𝔲_{0}$ and $𝔲_{1}$ . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of $S L_{2}$ -representations,...

On the Burns-Epstein invariants of spherical CR 3-manifolds

Khoi The Vu (2011)

Annales de l’institut Fourier

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In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As an application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.

Elementary linear algebra for advanced spectral problems

Johannes Sjöstrand, Maciej Zworski (2007)

Annales de l’institut Fourier

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We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations and numerical analysis. Under the name of the Schur complement method it is one of the standard tools of applied linear algebra. In PDE and spectral analysis it is sometimes called the Grushin problem method, and here we concentrate on its uses in the study of infinite dimensional problems, coming from partial differential operators...