Related papers: Autoconjugate representers for linear monotone ope…

Maximally monotone operators play important roles in optimization, variational analysis and differential equations. Finding zeros of maximally monotone operators has been a central topic. In a Hilbert space, we show that most resolvents are…

We introduce the resolvent composition, a monotonicity-preserving operation between a linear operator and a set-valued operator, as well as the proximal composition, a convexity-preserving operation between a linear operator and a function.…

In this paper we initiate the study of real operator monotonicity for functions of tuples of operators, which are multivariate structured maps with a functional calculus called free functions that preserve the order between real parts (or…

We study the homogenization of a stationary random maximal monotone operator on a probability space equipped with an ergodic dynamical system. The proof relies on Fitzpatrick's variational formulation of monotone relations, on Visintin's…

Let $f$ be a function on ${\Bbb R}^2$ in the inhomogeneous Besov space $B_{\infty,1}^1({\Bbb R}^2)$. For a pair $(A,B)$ of not necessarily bounded and not necessarily commuting self-adjoint operators, we define the function $f(A,B)$ of $A$…

We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential…

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…

The operator monotone functions defined in the positive half-line are of particular importance. We give a version of the theory in which integral representations for these functions can be established directly without invoking L\"owner's…

In this paper we study, in the relaxed context of locally convex spaces, intrinsic properties of monotone operators needed for the sum conjecture for maximal monotone operators to hold under classical interiority-type domain constraints.

Finite Cartesian products of operators play a central role in monotone operator theory and its applications. Extending such products to arbitrary families of operators acting on different Hilbert spaces is an open problem, which we address…

Using the theory of Hilbert direct integrals, we introduce and study a monotonicity-preserving operation, termed the integral resolvent mixture. It combines arbitrary families of monotone operators acting on different spaces and linear…

We present a new sufficient condition under which a maximal monotone operator $T:X\tos X^*$ admits a unique maximal monotone extension to the bidual $\widetilde T:X^{**} \rightrightarrows X^*$. For non-linear operators this condition is…

This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex…

The theory of monotone operators plays a major role in modern optimization and many areas of nonlinera analysis. The central classes of monotone operators are matrices with a positive semidefinite symmetric part and subsifferential…

We study the behaviour of functions of pairs of commuting self-adjoint operators under perturbations by relatively bounded operators. We obtain analogs of our earlier results for functions of a single self-adjoint operator under relatively…

Monotone convex operators and time-consistent systems of operators appear naturally in stochastic optimization and mathematical finance in the context of pricing and risk measurement. We study the dual representation of a monotone convex…

In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves…

We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the…

Non-trivial analysis problems require posets with infinite ascending and descending chains. In order to compute reasonably precise post-fixpoints of the resulting systems of equations, Cousot and Cousot have suggested accelerated fixpoint…

This paper intends to lay the theoretical foundation for the method of functional maps, first presented in 2012 by Ovsjanikov, Ben-Chen, Solomon, Butscher and Guibas in the field of the theory and numerics of maps between shapes. We show…