2024/10/25 by Luis A. Cedeño-Pérez, Hernando Quevedo, Cedeño-Pérez, Luis A. +1
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2410.19306
openalex publication_date 2024/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a new kind of measures, called projection families, which generalize the classical notion of vector and operator-valued measures. The maximal class of reasonable functions admits an integral with respect to a projection family, where the integral is defined as an element of the second dual instead of the original space. We show that projection families possess strong enough properties to satisfy the theorems of Monotone Convergence and Dominated convergence, but are much easier to come by than the more restrictive operator-valued measures.