Let D be a Dirac type operator on a compact manifold M and let Σ be a Lipschitz submanifold of codimension one partitioningM into two Lipschitz domains Ω±. Also, let Hp±(Σ, D) be the traces on Σ of the (Lpstyle) Hardy spaces associated with D in Ω±. Then (Hp−(Σ, D),Hp+(Σ, D)) is a Fredholm pair of subspaces for Lp(Σ) (in Kato’s sense) whose index is the same as the index of the Dirac operator D...

Let $(M,g)$ be a pseudo-Riemannian manifold of signature $(p,q)$. We compute the obstruction for vector bundle $S$ over to admit Dirac operator whose principal symbol induces on structure irreducible real Clifford modules complex type, that is, spinor type. In order do this, we use theory Lipschitz structures in $p-q\equiv_8 3,7$ reformulate problem as $\mathrm{Spin}^{o}_{\alpha}$ with $\alpha ...

On a bounded strongly pseudo-convex domain X in C with a Lipschitz boundary, we prove that the ∂̄−Neumann operator N can be extended as a bounded operator from Sobolev (−1/2)−spaces to the Sobolev (1/2)−spaces. In particular, N is compact operator on Sobolev (−1/2)−spaces.

It is shown that a locally Lipschitz function is approximately convex if, and only if, its Clarke subdifferential is a submonotone operator. Consequently, in finite dimensions, the class of locally Lipschitz approximately convex functions coincides with the class of lower-C functions. Directional approximate convexity is introduced and shown to be a natural extension of the class of lower-C fun...

In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of D...

We study the spectrum of Robin Laplacian with a complex parameter $$\alpha $$ on bounded Lipschitz domain $$\Omega . start by establishing number properties corresponding operator, such as generation properties, analytic dependence eigenvalues and eigenspaces \in {\mathbb {C}}$$ , basis eigenfunctions. Our focus, however, is bounds asymptotics for functions : we providing estimates numerical ra...