2025/10/10 by Sotiris Armeniakos, Armeniakos, Sotiris, Aris Daniilidis +1
Mathematics · #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2510.09368
openalex created_date 2025/10/10 · openalex publication_date 2025/10/10 · openalex updated_date 2026/07/28
We study maximal monotone operators A : X \rightrightarrows X^* whose Fitzpatrick family reduces to a singleton; such operators will be called uniquely representable. We show that every such operator is cyclically monotone (hence, A=∂ f for some convex function f) if and only if it is 3-monotone. In Radon-Nikodým spaces, under mild conditions (which become superfluous in finite dimensions), we prove that a subdifferential operator A=∂ f is uniquely representable if and only if f is the sum of a support and an indicator function of suitable convex sets.