Related papers: Divided difference operators on polytopes
The existence of uniformly bounded discrete extension operators is established for conforming Raviart-Thomas and N\'ed\'elec discretisations of $H(div)$ and $H(curl)$ on locally refined partitions of a polyhedral domain into tetrahedra.
For any Coxeter system, and any double coset for two standard parabolic subgroups, we introduce a Demazure operator. These operators form a basis for morphism spaces in a category we call the nilCoxeter category, and we also present this…
For an untwisted affine Kac-Moody Lie algebra $\mathfrak{g}$ with Cartan and Borel subalgebras $\mathfrak{h} \subset \mathfrak{b} \subset \mathfrak{g}$, affine Demazure modules are certain $U(\mathfrak{b})$-submodules of the irreducible…
We represent a bilinear Calder\'on-Zygmund operator at a given smoothness level as a finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and continuous paraproduct forms. This representation results in a…
With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…
A differential geometrical and topological structure of Delsarte transmutation operators in multidimension is studied, the relationships with De Rham-Hodge-Skrypnik theory of generalized differential complexes is stated.
Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those in terms of Euler operators obtained from the variational…
Many (if not most) of convex polytopes, important for combinatorial and algebraic geometry, are closely related to secondary polytopes of point configurations, or base polytopes of submodular functions, or their numerous variations and…
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…
This article is about a decoding algorithm for error-correcting subspace codes. A version of this algorithm was previously described by Rosenthal, Silberstein and Trautmann. The decoding algorithm requires the code to be defined as the…
An elliptic theory is constructed for operators acting in subspaces defined via odd pseudodifferential projections. Subspaces of this type arise as Calderon subspaces for first order elliptic differential operators on manifolds with…
This paper investigates the representation theory of the algebra of partially transposed permutation operators, $\mathcal{A}^d_{p,p}$, which provides a matrix representation for the abstract walled Brauer algebra. This algebra has recently…
We construct a divided difference operator using GKM theory. This generalizes the classical divided difference operator for the cohomology of the complete flag variety. This construction proves a special case of a recent conjecture of…
We obtain a family of functional identities satisfied by vector-valued functions of two variables and their geometric inversions. For this we introduce particular differential operators of arbitrary order attached to Gegenbauer polynomials.…
Differential operators on Schwartz distributions conventionally are defined as the transpose of differential operators on functions with compact support. They do not exhaust all differential operators. We follow algebraic formalism of…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
We introduce a deformed product construction for simple polytopes in terms of lower-triangular block matrix representations. We further show how Gale duality can be employed for the construction and for the analysis of deformed products…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
We utilize group-theoretical methods to develop a matrix representation of differential operators that act on tensors of any rank. In particular, we concentrate on the matrix formulation of the curl operator. A self-adjoint matrix of the…
We introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry…