Finite difference calculus in the continuum

2024/10/31 by Dmitri Finkelshtein, Yuri Kondratiev, Finkelshtein, Dmitri +5
Mathematics · #05A10 #05A40 #47B39 #47B93 #60G55 #60J25 #81S05 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2410.23847

openalex publication_date 2024/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

The paper describes known and new results about finite difference calculus on configuration spaces. We describe finite difference geometry on configuration spaces, connect finite difference operators with cannonical commutation relations, find explicit form for certain finite difference Markov generators on configuration spaces, and describe spaces of Newton series defined over the configuration spaces.

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