Comptes Rendus
Analyse fonctionnelle
A new proof of the GGR conjecture
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 349-353.

For each positive integer n, function f, and point x, the 1998 conjecture by Ginchev, Guerragio, and Rocca states that the existence of the nth Peano derivative f (n) (x) is equivalent to the existence of all n(n+1)/2 generalized Riemann derivatives,

D k,-j f(x)=lim h0 1 h n i=0 k (-1) i k if(x+(k-i-j)h),

for j,k with 0j<kn. A version of it for n2 replaces all -j with j and eliminates all j=k-1. Both the GGR conjecture and its version were recently proved by the authors using non-inductive proofs based on highly non-trivial combinatorial algorithms. This article provides a second, inductive, algebraic proof to each of these theorems, based on a reduction to (Laurent) polynomials.

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DOI : 10.5802/crmath.413
Classification : 26A24, 13F20, 15A03, 26A27

J. Marshall Ash 1 ; Stefan Catoiu 1 ; Hajrudin Fejzić 2

1 Department of Mathematics, DePaul University, Chicago, IL 60614
2 Department of Mathematics, California State University, San Bernardino, CA 92407
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {A new proof of the {GGR} conjecture},
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J. Marshall Ash; Stefan Catoiu; Hajrudin Fejzić. A new proof of the GGR conjecture. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 349-353. doi : 10.5802/crmath.413. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.413/

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