Infinite derivatives versus integral operators
Published on:
1 February 2023
Primary Category:
High Energy Physics - Theory
Paper Authors:
Carlos Heredia,
Josep Llosa
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Key Details
Infinite derivatives and integral operators yield different results when acting on some smooth functions
Integral operators have a wider domain of applicability than infinite derivatives
Infinite derivative operators can be ill-defined even for simple smooth functions
The domains only fully agree for entire functions with infinite radius of convergence
Numerical simulations confirm divergence of infinite derivative series
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AI generated summary
Infinite derivatives versus integral operators
This paper analyzes the relationship between nonlocal field theories formulated with either infinite derivatives or integral operators. It focuses on the operators that appear in p-adic string theory and noncommutative field theories. The authors prove that infinite derivative operators are not always well-defined when acting on smooth, compact support functions, demonstrating an inconsistency compared to the integral operator formulation. They conclude integral operators have a wider domain of applicability.
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