Related papers: Differential operator Dirac structures
Differential operators acting on functions defined on graphs by different studies do not form a consistent framework for the analysis of real or complex functions in the sense that they do not satisfy the Leibniz rule of any order. In this…
Complete spectra of the staggered Dirac operator $\Dirac$ are determined in four-dimensional $SU(2)$ gauge fields with and without dynamical fermions. An attempt is made to relate the performance of multigrid and conjugate gradient…
For permutations $v,w \in \mathfrak S_n$, Macdonald defines the skew divided difference operators $\partial_{w/v}$ as the unique linear operators satisfying $\partial_w(PQ) = \sum_v v(\partial_{w/v}P) \cdot \partial_vQ$ for all polynomials…
Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show thatthey are the skew symplectic and skew orthogonal Schur polynomials defined implicitly by…
Theory of differential operators on associative algebras is not extended to the non-associative ones in a straightforward way. We consider differential operators on Lie algebras. A key point is that multiplication in a Lie algebra is its…
In this paper we study the self-adjointness and spectral properties of two-dimensional Dirac operators with electrostatic, Lorentz scalar, and anomalous magnetic $\delta$-shell interactions with constant weights that are supported on a…
We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single…
The second order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin-manifold. It is shown that the operator is defined in terms of…
In this paper we extend the previously introduced class of boundary port-Hamiltonian systems to boundary control systems where the variational derivative of the Hamiltonian functional is replaced by a pair of reciprocal differential…
This paper deals with an inverse nodal problem for the Dirac differential operator with the discontinuity conditions inside the interval. We obtain a new approach for asymptotic expressions of the solutions and prove that the coefficients…
A non-classical Weyl theory is developed for skew-self-adjoint Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and direct and inverse problems are solved. A Borg-Marchenko type uniqueness…
This paper considers averaging operators on various algebraic structures and studies the induced structures. We first introduce the notion of an averaging operator on a group $G$ and show that it induces a rack structure. Moreover, the…
In these notes, we present an alternative version of discrete Dirac mechanics using Dirac structures. We first establish a notion of 'continuous Dirac system' and then propose a definition of discrete Dirac system, proving that it is…
In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…
This paper is devoted to the study of the spectral properties of Dirac operators on the three-sphere with singular magnetic fields supported on smooth, oriented links. As for Aharonov-Bohm solenoids in Euclidean three-space, the flux…
We study three practical implementations of the Overlap-Dirac operator $D_o= (1/2) [1 + \gamma_5\epsilon(H_w)]$ in four dimensions. Two implementations are based on different representations of $\epsilon(H_w)$ as a sum over poles. One of…
The recently introduced concept of a spectral shift operator is applied in several instances. Explicit applications include Krein's trace formula for pairs of self-adjoint operators, the Birman-Solomyak spectral averaging formula and its…
We propose an operadic framework suitable for describing algebraic structures with operations being multilinear differential operators of varying orders or, more generally, formal series of such operators. The framework is built upon the…
We study the phenomena that arise when we combine the standard pseudodifferential operators with those operators that appear in the study of some sub-elliptic estimates, and on strongly pseudoconvex domains. The algebra of operators we…