Hybrid transforms of constructible functions - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Foundations of Computational Mathematics Year : 2022

Hybrid transforms of constructible functions

Abstract

We introduce a general definition of hybrid transforms for constructible functions. These are integral transforms combining Lebesgue integration and Euler calculus. Lebesgue integration gives access to well-studied kernels and to regularity results, while Euler calculus conveys topological information and allows for compatibility with operations on constructible functions. We conduct a systematic study of such transforms and introduce two new ones: the Euler-Fourier and Euler-Laplace transforms. We show that the first has a left inverse and that the second provides a satisfactory generalization of Govc and Hepworth's persistent magnitude to constructible sheaves, in particular to multi-parameter persistent modules. Finally, we prove index-theoretic formulae expressing a wide class of hybrid transforms as generalized Euler integral transforms. This yields expectation formulae for transforms of constructible functions associated to (sub)level-sets persistence of random Gaussian filtrations.
Fichier principal
Vignette du fichier
main.pdf (5.29 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03474277 , version 1 (30-01-2023)

Licence

Attribution

Identifiers

Cite

Vadim Lebovici. Hybrid transforms of constructible functions. Foundations of Computational Mathematics, 2022, ⟨10.1007/s10208-022-09596-2⟩. ⟨hal-03474277⟩
75 View
15 Download

Altmetric

Share

Gmail Facebook X LinkedIn More