Harmonic analysis on nilmanifolds
نویسندگان
چکیده
منابع مشابه
Harmonic Analysis on Heisenberg Nilmanifolds
In these lectures we plan to present a survey of certain aspects of harmonic analysis on a Heisenberg nilmanifold Γ\Hn. Using Weil-Brezin-Zak transform we obtain an explicit decomposition of L(Γ\H) into irreducible subspaces invariant under the right regular representation of the Heisenberg group. We then study the Segal-Bargmann transform associated to the Laplacian on a nilmanifold and charac...
متن کاملSymplectically Harmonic Cohomology of Nilmanifolds
which is a symplectic analog of the well-known de Rham–Hodge ∗operator on oriented Riemannian manifolds: one should use the symplectic form instead of the Riemannian metric. Going further, one can define operator δ = ± ∗ d∗, δ = 0. The form α is called symplectically harmonic if dα = 0 = δα. However, unlike de Rham–Hodge case, there exist simplectically harmonic forms which are exact. Because o...
متن کاملTopological Dynamics on Nilmanifolds
There has always been a lack of examples of compact manifolds which are minimal sets under the action of the real line, minimal meaning that each orbit is dense in the manifold. All tori admit such an action and G. A. Hedlund [4] has given examples of 3-manifolds having such an action. The action of a group T on a metric space X is said to be distal if for any two distinct points x, y&X the dis...
متن کاملMinimal Metrics on Nilmanifolds
A left invariant metric on a nilpotent Lie group is called minimal, if it minimizes the norm of the Ricci tensor among all left invariant metrics with the same scalar curvature. Such metrics are unique up to isometry and scaling and the groups admitting a minimal metric are precisely the nilradicals of (standard) Einstein solvmanifolds. If N is endowed with an invariant symplectic, complex or h...
متن کاملEquidistribution of Sparse Sequences on Nilmanifolds
We study equidistribution properties of nil-orbits when the time parameter is restricted to the range of some sparse sequence that is not necessarily polynomial. For example, we show that if X = G/Γ is a nilmanifold, b ∈ G is an ergodic nilrotation, and c ∈ R \ Z is positive, then the sequence (b cΓ)n∈N is equidistributed in X. This is also the case when n c is replaced with a(n), where a(t) is...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1970
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1970-0279244-3