2019/01/25 by Isaac Z. Pesenson, Pesenson, Isaac Z.
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1901.08726
openalex publication_date 2019/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the framework of a strictly local regular Dirichlet space \bf X we introduce the subspaces PWω,>>ω>0, of Paley-Wiener functions of bandwidth ω. It is shown that every function in PWω,>>ω>0, is uniquely determined by its average values over a family of balls B(xj, ρ),>xj∈ \bf X, which form an admissible cover of \bf X and whose radii are comparable to ω-1/2. The entire development heavily depends on some local and global Poincaré-type inequalities. In the second part of the paper we realize the same idea in the setting of a weighted combinatorial finite or infinite countable graph G. We have to treat the case of graphs separately since the Poincaré inequalities we are using on them are somewhat different from the Poincaré inequalities in the first part.