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A Covering Lemma on the Unit Sphere and Application to the Fourier–Laplace Convergence

✍ Scribed by Rong Huang*; Kun Yang Wang**

Book ID
106278078
Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
2007
Tongue
English
Weight
153 KB
Volume
23
Category
Article
ISSN
1439-7617

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On a new form of the ergodic theorem for
On a new form of the ergodic theorem for the unit sphere with application to spectral theory
✍ Liangpan Li; Lan Tang 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 133 KB 👁 1 views

## Abstract Let 1 ≤ __p__ < ∞ and let __T__ be an ergodic measure‐preserving transformation of the finite measure space (__X__, __μ__). The classical __L^p^__ ergodic theorem of von Neumann asserts that for any __f__ ϵ __L^p^__ (__X__, __μ__), equation image When __X__ = 𝕊^__n__^ (the unit spher