 Embedded trace operator for infinite metric treesValentina Franceschi, Kiyan Naderi and Konstantin Pankrashkin Mathematische Nachrichten, 2025, vol. 298, issue 1, 190-243 Abstract: We consider a class of infinite weighted metric trees obtained as perturbations of self‐similar regular trees. Possible definitions of the boundary traces of functions in the Sobolev space on such a structure are discussed by using identifications of the tree boundary with a surface. Our approach unifies some constructions proposed by Maury, Salort, and Vannier for discrete weighted dyadic trees (expansion in orthogonal bases of harmonic functions on the graph and using Haar‐type bases on the domain representing the boundary), and by Nicaise and Semin and Joly, Kachanovska, and Semin for fractal metric trees (approximation by finite sections and identification of the boundary with a interval): We show that both machineries give the same trace map, and for a range of parameters we establish the precise Sobolev regularity of the traces. In addition, we introduce new geometric ingredients by proposing an identification with arbitrary Riemannian manifolds. It is shown that any compact manifold admits a suitable multiscale decomposition and, therefore, can be identified with a metric tree boundary in the context of trace theorems. Date: 2025 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:298:y:2025:i:1:p:190-243 Ordering information: This journal article can be ordered from Access Statistics for this article Mathematische Nachrichten is currently edited by Robert Denk More articles in Mathematische Nachrichten from Wiley Blackwell |
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