相关论文: Structure theorems for linear and non-linear diffe…
New finite-dimensional representations of specific polynomial deformations of sl(2,R) are constructed. The corresponding generators can be, in particular, realized through linear differential operators preserving a finite-dimensional…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
We present some fundamental results on (possibly nonlinear) algebraic semigroups and monoids. These include a version of Chevalley's structure theorem for irreducible algebraic monoids, and the description of all algebraic semigroup…
In this paper we study the map associating to a linear differential operator with rational coefficients its monodromy data. The operator has one regular and one irregular singularity of Poincare' rank 1. We compute the Poisson structure of…
The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital…
We study a notion of indecomposability in differential algebraic groups which is inspired by both model theory and differential algebra. After establishing some basic definitions and results, we prove an indecomposability theorem for…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
Nonlinear ordinary differential equations can rarely be solved analytically. Koopman operator theory provides a way to solve nonlinear systems by mapping nonlinear dynamics to a linear space using eigenfunctions. Unfortunately, finding such…
We use homotopy operators for the $L_\infty$-algebra associated with an equivariant deformation problem in order to describe a smooth parametrization of the space of structures around a given one. Along the way we give new algebraic and…
Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics we…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
Following the classical approach of P\'olya-Schur theory we initiate in this paper the study of linear operators acting on $\mathbb{R}[x]$ and preserving either the set of positive univariate polynomials or similar sets of non-negative and…
We establish operator structure identities for quantum channels and their error-correcting and private codes, emphasizing the complementarity relationship between the two perspectives. Relevant structures include correctable and private…
This paper develops a nonlinear operator dynamic that progressively removes the influence of a prescribed feature subspace while retaining maximal structure elsewhere. The induced sequence of positive operators is monotone, admits an exact…
We study large linear structures inside sets arising in the theory of norm-attaining operators. We provide several results in the context of lineability, spaceability, maximal-spaceability, and $(\alpha, \beta)$-spaceability for sets of…
In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of…
In a recent paper [J.Math.Phys. vol42, 2236-2265 (2001)], we discussed differential operators within a quaternionic formulation of quantum mechanics. In particular, we proposed a practical method to solve quaternionic and complex linear…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
This work deals with the problem of designing observers for the estimation of a single function of the states for discrete-time nonlinear systems. Necessary and sufficient conditions for the existence of lower order functional observers…
Let k be an algebraically closed field. Using the Eilenberg-Watts theorem over schemes, we determine the structure of k-linear right exact direct limit and coherence preserving functors from the category of quasi-coherent sheaves on P^1_k…