Related papers: Sub-Dirac operators, spectral Einstein functionals…
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
In this work, we consider Dirac-type operators with a constant delay less than half of the interval and not less than two-fifths of the interval. For our considered Dirac-type operators, two inverse spectral problems are studied.…
We present the details of our embedding proof of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary.
A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra and eigenfunctions of a family of…
We use the Dirac operator technique to establish sharp distance estimates for compact spin manifolds under lower bounds on the scalar curvature in the interior and on the mean curvature of the boundary. In the situations we consider, we…
We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class generalizing that of Killing spinors. We…
We compute the spectrum of the Dirac operator on 3-dimensional Heisenberg manifolds. The behavior under collapse to the 2-torus is studied. Depending on the spin structure either all eigenvalues tend to $\pm\infty$ or there are eigenvalues…
In this paper, we get estimates on the higher eigenvalues of the Dirac operator on locally reducible Riemannian manifolds, in terms of the eigenvalues of the Laplace-Beltrami operator and the scalar curvature. These estimates are sharp, in…
In this paper inverse problems for Dirac operator with nonlocal conditions are considered. Uniqueness theorems of inverse problems from the Weyl-type function and spectra are provided, which are generalizations of the well-known Weyl…
We show meromorphic extension and analyze the divisors of a Selberg zeta function of odd type $Z_{\Gamma,\Sigma}^{\rm o}(\lambda)$ associated to the spinor bundle $\Sigma$ on odd dimensional convex co-compact hyperbolic manifolds…
We investigate the properties of the Dirac operator on manifolds with boundaries in presence of the Atiyah-Patodi-Singer boundary condition. An exact counting of the number of edge states for boundaries with isometry of a sphere is given.…
A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all the tools of noncommutative geometry. In particular, we apply this to the N=1 supersymmetric non-linear sigma…
Spectral boundary conditions for Laplace-type operators, of interest in string and brane theory, are partly Dirichlet, partly Neumann-type conditions, partitioned by a pseudodifferential projection. We give sufficient conditions for…
Properties of the Cauchy-Riemann-Fueter equation for maps between quaternionic manifolds are studied. Spaces of solutions in case of maps from a K3-surface to the cotangent bundle of a complex projective space are computed. A relationship…
We construct a canonical geometrically realised Connes spectral triple or `Dirac operator' $D\!\!\!/$ from the data of a quantum metric $g\in \Omega^1\otimes_A\Omega^1$ and quantum Levi-Civita bimodule connection, at the pre-Hilbert space…
This paper is related to an inverse problem for a class of Dirac operators with discontinuous coefficient and eigenvalue parameter contained in boundary conditions. The asymptotic formula of eigenvalues of this problem is examined. The…
By using the Ljusternik-Schnirelman principle, we establish the existence of a nondecreasing sequence of nonnegative eigenvalues for the p-Dirac operator on compact spin manifold. Using the biorthogonal system theory on separable Banach…
Let $M$ be an orientable compact flat Riemannian manifold endowed with a spin structure. In this paper we determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles of $M$, and we derive a formula for the…
The magnetic Dirac operator describes the relativistic motion of a charged particle in a magnetic field. Although this operator got a lot of attention in physics many of its fundamental mathematical properties remain unexplored and this…
We review the spectral flow techniques for computing the index of the overlap Dirac operator including results relevant for SUSY Yang-Mills theories. We describe properties of the overlap Dirac operator, and methods to implement it…