Dynamics of $ L^p $ multipliers on harmonic manifolds
نویسندگان
چکیده
<abstract><p>Let $ X be a complete, simply connected harmonic manifold of purely exponential volume growth. This class contains all non-flat manifolds nonpositive curvature, and in particular known examples non-compact except for the flat spaces. We use Fourier transform from <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup> to investigate dynamics on L^p(X) p &gt; 2 certain bounded linear operators T : \to which we call "$ L^p $-multipliers" accordance with standard terminology. Examples $-multipliers are given by operator convolution an L^1 radial function, or more generally finite measure. In elements heat semigroup e^{t\Delta} act as multipliers. Given &lt; \infty $, show that any $-multiplier is not scalar multiple identity, there open set values \nu \in {\mathbb C} \frac{1}{\nu} chaotic sense Devaney, i.e., topologically transitive periodic points dense. Moreover such mixing. also constant c_p 0 c \operatorname{Re} action shifted e^{ct} chaotic. These results generalize corresponding rank one symmetric spaces noncompact type NA groups (or Damek-Ricci spaces).</p></abstract>
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ژورنال
عنوان ژورنال: Electronic research archive
سال: 2022
ISSN: ['2688-1594']
DOI: https://doi.org/10.3934/era.2022154