Some nonlocal formulas inspired by an identity of James Simons

Inspired by a classical identity proved by James Simons, we establish a new geometric formula in a nonlocal, possibly fractional, setting. Our formula also recovers the classical case in the limit, thus providing an approach to Simons' work that does not heavily rely on differential geometry.

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Publication Details

Journal
URN:NBN Resolver for Germany & Switzerland (German National Library)
Published
2025-11-12
DOI
https://doi.org/10.17879/11958511860
Primary Topic
Functional Equations Stability Results
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article
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article

Some nonlocal formulas inspired by an identity of James Simons

S. (Serena) Dipierro, E. (Enrico) Valdinoci, J. (Jack) Thompson
URN:NBN Resolver for Germany & Switzerland (German National Library)
Functional Equations Stability Results
article

Some nonlocal formulas inspired by an identity of James Simons

S. (Serena) Dipierro, E. (Enrico) Valdinoci, J. (Jack) Thompson
article en

Abstract

Inspired by a classical identity proved by James Simons, we establish a new geometric formula in a nonlocal, possibly fractional, setting. Our formula also recovers the classical case in the limit, thus providing an approach to Simons' work that does not heavily rely on differential geometry.

URN:NBN Resolver for Germany & Switzerland (German National Library)
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Functional Equations Stability Results
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Some nonlocal formulas inspired by an identity of James Simons — S. (Serena) Dipierro, E. (Enrico) Valdinoci, et al. · URN:NBN Resolver for Germany & Switzerland (German National Library) (2025) | TGRS Research Map | TGRS