A Theorem of Roe and Strichartz on homogeneous trees

2019/08/16 by Pratyoosh Kumar, Kumar, Pratyoosh, Sumit Kumar Rano +1
Mathematics · #20E08 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 43A85 Secondary 39A12 #math.FA #msc:20E08 #msc:39A12 #msc:43A85

paper · pdf · doi:10.48550/arxiv.1908.05998

15 PAGES

arxiv created 2019/08/16 · arxiv updated 2019/08/19

Abstract

In 1980, J. Roe proved that if \f_k\_k∈ℤ is doubly infinite sequence of functions in ℝ which is uniformly bounded and satisfies (df_k/dx)=f_k+1 for all k∈ℤ then f₀(x)=asin(x+θ) for some a,θ∈ℝ. Later in 1993 Strichartz suitably extended the above result to ℝⁿ. In this article we prove a version of their result for homogeneous trees.

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