Related papers: Boundary value problems with Atiyah-Patodi-Singer …
We study the Atiyah-Patodi-Singer (APS) index, and its equality to the spectral flow, in an abstract, functional analytic setting. More precisely, we consider a (suitably continuous or differentiable) family of self-adjoint Fredholm…
We show that the existence of a Fredholm element of the zero calculus of pseudodifferential operators on a compact manifold with boundary with a given elliptic symbol is determined, up to stability, by the vanishing of the Atiyah-Bott…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
We study the closed extensions (realizations) of differential operators subject to homogeneous boundary conditions on weighted L_p-Sobolev spaces over a manifold with boundary and conical singularities. Under natural ellipticity conditions…
We present the details of our embedding proof of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary.
We investigate an arbitrary regular elliptic boundary-value problem given in a bounded Euclidean domain with infinitely smooth boundary. We prove that the operator of the problem is bounded and Fredholm in appropriate pairs of H\"ormander…
We review the definition of a Lie manifold $(M, \VV)$ and the construction of the algebra $\Psi\sp{\infty}\sb{\VV}(M)$ of pseudodifferential operators on a Lie manifold $(M, \VV)$. We give some concrete Fredholmness conditions for…
Along the lines of the classic Hodge-De Rham theory a general decomposition theorem for sections of a Dirac bundle over a compact Riemannian manifold is proved by extending concepts as exterior derivative and coderivative as well as as…
We derive conditions that ensure the existence of a bounded $H_\infty$-calculus in weighted $L_p$-Sobolev spaces for closed extensions $\underline{A}_T$ of a differential operator $A$ on a conic manifold with boundary, subject to…
On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that the Atiyah-Singer Dirac operator $\mathrm{D}_{\mathcal B}$ in $\mathrm{L}^{2}$ depends Riesz continuously on $\mathrm{L}^{\infty}$ perturbations…
We study the index of the APS boundary value problem for a strongly Callias-type operator D on a complete Riemannian manifold $M$. We show that this index is equal to an index on a simpler manifold whose boundary is a disjoint union of two…
We investigate manifolds with boundary in noncommutative geometry. Spectral triples associated to a symmetric differential operator and a local boundary condition are constructed. For a classical Dirac operator with a chiral boundary…
We study a Dirac operator subject to Atiayh-Patodi-Singer like boundary conditions on the solid torus and show that the corresponding boundary value problem is elliptic, in the sense that the Dirac operator has a compact parametrix.
We study the Cauchy data spaces of the strongly Callias-type operators using maximal domain on manifolds with non-compact boundary, with the aim of understanding the Atiyah-Patodi-Singer index and elliptic boundary value problems.
A regular elliptic boundary-value problem over a bounded domain with a smooth boundary is studied. We prove that the operator of this problem is a Fredholm one in the two-sided refined scale of the functional Hilbert spaces and generates a…
We consider Dirac-type operators on manifolds with boundary, and set out to determine all local smooth boundary conditions that give rise to (strongly) regular self-adjoint operators. By combining the general theory of boundary value…
The Atiyah-Singer index theorem on a closed manifold is well understood and appreciated in physics. On the other hand, the Atiyah-Patodi-Singer index, which is an extension to a manifold with boundary, is physicist-unfriendly, in that it is…
Functional determinants for Dirac operators on manifolds with boundary are considered. Ellipticity of boundary value problems is discussed in terms of the Calderon projector. The functional determinant for a Dirac operator on a…
We introduce and study a general pseudodifferential calculus for boundary value problems on a class of non-compact manifolds with boundary (so-called Lie manifolds with boundary). This is accomplished by constructing a suitable…
For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the…