Related papers: Differential Invariants and Construction of Condit…
In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an extension of the Lueders - von Neumann measurement to…
A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.
We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical…
We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…
This thesis is concerned with the theory of invariant bilinear differential pairings on parabolic geometries. It introduces the concept formally with the help of the jet bundle formalism and provides a detailed analysis. More precisely,…
Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…
We present initially the motivation, definition and basic properties of differential equations with proportional delay. In the last Section we present open problems.
The definition of the conditional probability is very important in the theory of the probability. This definition is based on the fact, that random events can be simultaneously measurable. This paper deal with the problem of conditioning…
The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…
We provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced. The boundary condition is allowed to be discontinuous and to depend…
In this article, we investigate differential operators on the Siegel-Jacobi space that are invariant under the natural action of the Jacobi group. These invariant differential operators play an important role in the arithmetic theory of…
Symmetry is present in many tasks in computer vision, where the same class of objects can appear transformed, e.g. rotated due to different camera orientations, or scaled due to perspective. The knowledge of such symmetries in data coupled…
This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
We show that, for both the conformal and projective groups, all the differential invariants of a generic surface in three-dimensional space can be written as combinations of the invariant derivatives of a single differential invariant. The…
In the present paper we start the systematic explicit construction of invariant differential operators by giving explicit description of one of the main ingredients - the cuspidal parabolic subalgebras. We explicate also the maximal…
The projection algorithm is frequently used in adaptive control and this note presents a detailed analysis of its properties.
We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.
In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional…
In this paper, we introduce the notion of conditional $h$-convex functions and we prove an operator version of the Jensen inequality for conditional $h$-convex functions. Using this type of functions, we give some refinements for Ky-Fan's…