Related papers: Commuting higher rank ordinary differential operat…
We outline the construction of differential invariants for higher--rank tensors.
In this paper we present a recurrent relation for counting meaningful compositions of the higher-order differential operations on the space $R^{n}$ (n=3,4,...) and extract the non-trivial compositions of order higher than two.
In this paper we study commuting difference operators containing a shift operator with only positive degrees. We construct examples of such operators in the case of hyperelliptic spectral curves.
In this paper we study rank two commuting ordinary differential operators with polynomial coefficients and the orbit space of the automorphisms group of the first Weyl algebra on such operators. We prove that for arbitrary fixed spectral…
The real theory of the Dunkl operators has been developed very extensively, while there still lacks the corresponding complex theory. In this paper we introduce the complex Dunkl operators for certain Coxeter groups. These complex Dunkl…
In this paper we study the subdifferential set of an operator. We give possible relation of the subdifferential set of an operator to that of its value, at a point where the operator attains its norm.
In this paper we develop the generalised Schur theory offered in the recent paper by the second author in dimension one case, and apply it to obtain a new explicit parametrisation of torsion free rank one sheaves on projective irreducible…
We introduce and fully analyze a new commutation relation $\overline{K} L_1 = L_2 K$ between finite convolution integral operator $K$ and differential operators $L_1$ and $L_{2}$, that has implications for spectral properties of $K$. This…
We first study some properties of images of commuting differential operators of polynomial algebras of order one with constant leading coefficients. We then propose what we call the image conjecture on these differential operators and show…
We indicate smooth real commuting matrix differential operators whose eigenvalues and eigenfunctions are parametrized by two-dimensional principally polarized abelian varieties.
We construct discrete analogues of the Dixmier operators, that is, commuting difference operators corresponding to a spectral curve of genus 1 whose coefficients are polynomials of the discrete variable.
We study the algebra of invariant differential operators on a certain homogeneous vector bundle over a Riemannian symmetric space of type $A_2$. We computed radial parts of its generators explicitly to obtain matrix-valued commuting…
We define the concept of completely regular ordinary differential operators and give various criteria for operators to belong to this class. We give also criteria for Birkhof regularity of ordinary differential operators in terms of the…
This paper presents an algebraic approach to characterizing higher-order differential operators. While the foundational Leibniz rule addresses first-order derivatives, its extension to higher orders typically involves identities relating…
Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider $P$ and $X$…
In the literature, we have several results associated with canonical decomposition of commuting contractions. In this paper, we generalize a few of these results to $Q$-commuting contractions. Here we mainly deal with $Q$-commuting and…
We construct new examples of multidimensional commuting matrix differential operators and a multidimensional analog of the Kadomtsev--Petviashvili hierarchy.
We consider four-dimensional Riemannian manifolds with commuting higher order Jacobi operators defined on two-dimensional orthogonal subspaces (polygons) and on their orthogonal subspaces. More precisely, we discuss higher order Jacobi…
This article explains the relationship between analytic and algebraic order in case of abstract pseudo-differential operators for a regular spectral triple.
We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates.