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math.FA2026
On the Spectral Synthesis of Lipschitz Vectorizations of Persistence Diagrams
Charles Fanning, Mehmet Emin Aktas
Persistence diagrams are fundamental descriptors in topological data analysis. Many statistical and machine learning methods require persistence diagrams to be mapped into vector s…
math.FA2026
Reproducing Kernel Hilbert Spaces on Banach Completions of Virtual Persistence Diagram Groups
Charles Fanning, Mehmet Aktas
Persistent homology maps a simplicial complex filtered by elements in to finite formal sums of elements of $\mathbb R_{\leq}^{2} = \{ (b,d) \in \mathbb R^2 \cup \{ \inf…