Related papers: Loops, Inverse Limits and Non-Determinism
Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…
This paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in…
Continuing the study of complexity theory of Koepke's Ordinal Turing Machines (OTMs) that was started by Rin, L\"owe and the author, we prove the following results: (1) An analogue of Ladner's theorem for OTMs holds: That is, there are…
This paper is concerned about the inverse coefficient problems of variable-coefficient fractional Schr\"{o}dinger equations with drift on connected closed Riemannian manifolds. We prove that the knowledge of the underlying equation of order…
We consider complex resonances for discrete and continuous Schr\"odinger operators, and we show that the resonances of discrete models converge to resonances of continuous models in the continuum limit. The potential is supposed to be a sum…
The classification of separable operator spaces and systems is commonly believed to be intractable. We analyze this belief from the point of view of Borel complexity theory. On one hand we confirm that the classification problems for…
We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity…
The decoherent histories approach to quantum theory is applied to a class of reparametrization invariant models, which includes systems described by the Klein-Gordon equation, and by a minisuperspace Wheeler-DeWitt equation. A key step in…
We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…
We develop a theoretical analysis for special neural network architectures, termed operator recurrent neural networks, for approximating nonlinear functions whose inputs are linear operators. Such functions commonly arise in solution…
We show that a densely defined closable operator $A$ such that the resolvent set of $A^2$ is not empty is necessarily closed. This result is then extended to the case of a polynomial $p(A)$. We also generalize a recent result by…
In this paper, we study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series, which we call the Wiener-Dirichlet algebra. We study the connection between the…
In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the…
We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…
We provide closed formulas for (unique) solutions of nonhomogeneous Dirichlet problems on balls involving any positive power $s>0$ of the Laplacian. We are able to prescribe values outside the domain and boundary data of different orders…
We show that a special case of the Feferman-Vaught composition theorem gives rise to a natural notion of automata for finite words over an infinite alphabet, with good closure and decidability properties, as well as several logical…
We present the two-loop corrected operator matrix elements calculated in N-dimensional regularization up to the finite terms which survive in the limit $\epsilon = N - 4 \to 0 $. The anomalous dimensions of the local operators have been…
We study properties of the topological space of composition operators on the Banach algebra of bounded functions on an unbounded, locally finite metric space in the operator norm topology and essential norm topology. Moreover, we…
An expansive, monotone operator is dominating; if it is also idempotent it is a closure operator. Although they have distinct properties, these two kinds of discrete operators are also intertwined. Every closure operator is dominating;…
In this paper we provide the resolvent computation of the parallel composition of a maximally monotone operator by a linear operator under mild assumptions. Connections with a modification of the warped resolvent are provided. In the…