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  • Contingent derivatives of the set-valued solution map of a noncoercive saddle point problem. A cross-fertilization between variational analysis and inverse problems
Title: Contingent derivatives of the set-valued solution map of a noncoercive saddle point problem. A cross-fertilization between variational analysis and inverse problems
Award ID(s):
1720067
PAR ID:
10166983
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Journal of Nonlinear and Variational Analysis
Volume:
4
Issue:
1
ISSN:
2560-6921
Page Range / eLocation ID:
127-134
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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    In this paper we show that every set A⊂ℕ with positive density contains B+C for some pair B,C of infinite subsets of ℕ, settling a conjecture of Erd\H os. The proof features two different decompositions of an arbitrary bounded sequence into a structured component and a pseudo-random component. Our methods are quite general, allowing us to prove a version of this conjecture for countable amenable groups. 
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