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We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single…
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…
In this paper, we examine a specific class of quadratic operators. For these operators, we identified all fixed points and categorized their types in the general case. Our analysis revealed that there are no attractive fixed points except…
A leading twist expansion in terms of bi-local operators is proposed for the structure functions of deeply inelastic scattering near the elastic limit $x \to 1$, which is also applicable to a range of other processes. Operators of…
Despite the broad use of fixed-point iterations throughout applied mathematics, the optimal convergence rate of general fixed-point problems with nonexpansive nonlinear operators has not been established. This work presents an acceleration…
The problem of phase space transport which is of interest both theoretically and from the point of view of applications has been investigated extensively using geometric and probabilistic methods. Two of the important tools for this that…
The role of the operator-product expansion in QCD calculations is discussed. Approximating the two-point correlation function by several terms and assuming an upper bound on the truncation error along the euclidean ray, we consider two…
We study if the parabolic forward-in-time maximal operator is bounded on parabolic BMO. It turns out that for non-negative functions the answer is positive, but the behaviour of sign changing functions is more delicate. The class parabolic…
We address the inverse Frobenius--Perron problem: given a prescribed target distribution $\rho$, find a deterministic map $M$ such that iterations of $M$ tend to $\rho$ in distribution. We show that all solutions may be written in terms of…
The Fourier operator truncated on a finite symmetric interval is considered. The limiting behavior of its spectrum is discussed as the length of the interval tends to infinity.
The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron Frobenius theory is developed in this differential framework to…
We study the dynamics of the Forced Logistic Map in the cylinder. We compute a bifurcation diagram in terms of the dynamics of the attracting set. Different properties of the attracting set are considered, as the Lyapunov exponent and, in…
We study the two-body Dirac operator in a bounded external field and for a class of unbounded pair-interaction potentials, both repulsive and attractive, including the Coulomb type. Provided the coupling constant of the pair-interaction…
There is constructed and considered the extension of classical Diriclet operator corresponding to uniformly log-concave measure in the space of symmetric differential forms. Sufficient conditions for its essential self-adjointness in…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…
We study Frobenius algebras of operator fields and introduce a novel notion of duality for them. We show that, under the assumption that the operator fields forming the Frobenius algebra are mutual symmetries, the operator fields in the…
Dynamical system-based linear transfer Perron- Frobenius (P-F) operator framework is developed to address analysis and design problems in the building system. In particular, the problems of fast contaminant propagation and optimal placement…
In this paper, we propose a data-driven approach for uncertainty propagation and reachability analysis in a dynamical system. The proposed approach relies on the linear lifting of a nonlinear system using linear Perron-Frobenius (P-F) and…
We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to…