Related papers: Rarita-Schwinger Type operators on Cylinders
This article develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is…
In this work, we analyze the combinatorial properties of cylinders and subdivisions of augmented semi-simplicial sets. These constructions are obtained as particular cases of a certain action from a co-semi-simplicial set on an augmented…
We analyze and compare the methods of construction of the recursion operators for a special class of integrable nonlinear differential equations related to A.III-type symmetric spaces in Cartan's classification and having additional…
The paper concerns the automorphism groups of Cayley graphs over cyclic groups which have a rational spectrum (rational circulant graphs for short). With the aid of the techniques of Schur rings it is shown that the problem is equivalent to…
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…
Several spectra of analytically Riesz operators will be characterized. These results will led to prove Weyl and Browder type theorems for the aforementioned class of operators.
This is a largely expository article based on our previous work on arithmetic diagonal cycles on unitary Shimura varieties. We define a class of Shimura varieties closely related to unitary groups which represent a moduli problem of abelian…
This paper studies the two-spinor form of the Rarita-Schwinger potentials subject to local boundary conditions compatible with local supersymmetry. The massless Rarita-Schwinger field equations are studied in four-real-dimensional…
This paper studies the two-component spinor form of massive spin-3/2 potentials in conformally flat Einstein four-manifolds. Following earlier work in the literature, a non-vanishing cosmological constant makes it necessary to introduce a…
The primary aim of this thesis is to investigate metrics which are induced by a differential form and arise as a critical point of Hitchin's variational principle. Firstly, we investigate metrics associated with the structure group PSU(3)…
In this paper we present two different problems within the framework of shift-invariant theory. First, we develop a triangular form for shift-preserving operators acting on finitely generated shift-invariant spaces. In case of the normal…
Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.
Integral categories were recently developed as a counterpart to differential categories. In particular, integral categories come equipped with an integration operator, known as an integral transformation, whose axioms generalize the basic…
Higher order higher spin operators are generalizations of $kth$-powers of the Dirac operator. In this paper, we study higher order higher spin operators defined on some conformally flat manifolds, namely cylinders and Hopf manifolds. We…
In [8] it was shown that the transplant operator transforms solutions of one Vekua equation into solutions of another Vekua equation, related to the first via a Schr\"odinger equation. In this paper we demonstrate a fundamental property of…
We define a class of pseudo-differential operators in a completely new way, which is called the abstract operators and expounded systematically the theory of abstract operators. By combining abstract operators with the Laplace transform, we…
By applying Ricceri's variational principle, we demonstrate the existence of solutions for the following Robin problem \begin{equation*}\left\{ \begin{array}{cc}-\func{div}\left( \omega _{1}(x)\left\vert \nabla u\right\vert^{p(x)-2}\nabla…
A classical result of Schubert calculus is an inductive description of Schubert cycles using divided difference (or push-pull) operators in Chow rings. We define convex geometric analogs of push-pull operators and describe their…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
Integral relations with the Cauchy kernel on a semi-axis for the Laguerre polynomials, the confluent hypergeometric function, and the cylindrical functions are derived. A part of these formulas is obtained by exploiting some properties of…