Related papers: Vector Differential Operators in arbitrary coordin…
We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of Caputo type.
We consider four combinatorial interpretations for the algebra of Boolean differential operators. We show that each interpretation yields an explicit matrix representation for Boolean differential operators.
We develop techniques useful for obtaining conformal blocks in embedding space. We construct a unique differential operator in embedding space and use it to construct a function that will be an important ingredient in assembling conformal…
This paper studies fractional integral operator for vector fields in weighted $L^1$. Using the estimates on fractional integral operator and Stein-Weiss inequalities, we can give a new proof for a class of Caffarelli-Kohn-Nirenberg…
Formulating boundary value problems for multidimensional partial derivative equations in terms of invariant operators of vector (tensor) analysis is convenient. Computational algorithms for approximate solutions are based on constructing…
Differential operators usually result in derivatives expressed as a ratio of differentials. For all but the simplest derivatives, these ratios are typically not algebraically manipulable, but must be held together as a unit in order to…
We prove that the Casimir operator acting on sections of a homogeneous vector bundle over a generalized flag manifold naturally extends to an invariant differential operator on arbitrary parabolic geometries. We study some properties of the…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.
The integral representation of Choquet operators defined on a space C(X) is established by using the Choquet-Bochner integral of a real-valued function with respect to a vector capacity.
In this paper, we define a differential operator as a modified Dirac operator. Using the operator, we introduce a quaternionic $k$-vector field on a quaternionic K\"{a}hler manifold and show that any quaternionic $k$-vector field…
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…
We pose a new algebraic formalism for studying differential calculus in vector bundles. This is achieved by studying various functors of differential calculus over arbitrary graded commutative algebras (DCGCA) and applying this language to…
Mathematical physics problems are often formulated using differential oprators of vector analysis - invariant operators of first order, namely, divergence, gradient and rotor operators. In approximate solution of such problems it is natural…
In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…
For a simple real Jordan algebra $V,$ a family of bi-differential operators from $\mathcal{C}^\infty(V\times V)$ to $\mathcal{C}^\infty(V)$ is constructed. These operators are covariant under the rational action of the conformal group of…
New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…
On the basis of the canonical quantization procedure of a system defined on a cubic lattice, we propose a new method, in which resolutions of unity expressed in terms of eigenvectors are naturally provided, to find eigenvectors of field…
We associate to an integral operator a discrete one which is conceptually simpler, and study the relations between them.