Related papers: Operator $\Delta-aS$ on warped product manifolds

In this paper we give sufficient conditions to obtain continuity results of solutions for the so called {\em $\phi-$Laplacian} $\Delta_\phi$ with respect to domain perturbations. We point out that this kind of results can be extended to a…

We study the index of the APS boundary value problem for a strongly Callias-type operator $D$ on a complete even dimensional Riemannian manifold $M$ (the odd dimensional case was considered in our previous paper arXiv:1706.06737). We use…

Let $\ell^p, 1\le p\le \infty$, be the space of all $p$-summable sequences and $C_a$ be the convolution operator associated with a summable sequence $a$. It is known that the $\ell^p$- stability of the convolution operator $C_a$ for…

In this paper, we consider a class of Hessian quotient equations in the warped product manifold $\overline{M}=I\times_{\lambda}M$. Under some sufficient conditions, we obtain an existence result for the star-shaped compact hypersurface…

We establish criteria for the stability of the essential spectrum for unbounded operators acting in Banach modules. The applications cover operators acting on sections of vector fiber bundles over non-smooth manifolds or locally compact…

In this note, we consider the space of all continuous operators with respect to the unbounded topology on locally solid vector lattices. We investigate whether this space forms a band. In addition, we look into some situations under which,…

Let $\Delta_{\Omega_\varepsilon}$ be the Dirichlet Laplacian in the domain $\Omega_\varepsilon:=\Omega\setminus\left(\cup_i D_{i \varepsilon}\right)$. Here $\Omega\subset\mathbb{R}^n$ and $\{D_{i \varepsilon}\}_{i}$ is a family of tiny…

We introduce a class of operators which is called unbounded Dunford-Pettis. In this paper, we study some properties of the operators, relationships with the other classes of operators and the space of these operators.

We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…

We show that the spectrum of the complex Laplacian on a product of hermitian manifolds is the Minkowski sum of the spectra of the complex Laplacians on the factors. We use this fact to show that the range of the d-bar operator on a product…

The fractional Laplacian $(-\Delta )^a$, $a\in(0,1)$, and its generalizations to variable-coefficient $2a$-order pseudodifferential operators $P$, are studied in $L_q$-Sobolev spaces of Bessel-potential type $H^s_q$. For a bounded open set…

In this article, we systematically investigate the stability properties of certain warped product Einstein manifolds. We characterize stability of these metrics in terms of an eigenvalue condition of the Einstein operator on the base…

We study closed extensions A of an elliptic differential operator on a manifold with conical singularities, acting as an unbounded operator on a weighted L_p-space. Under suitable conditions we show that the resolvent (\lambda-A)^{-1}…

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…

We give examples of spin $4$-manifolds with boundary $(M,\partial M)$ such that the boundary $\partial M$ has a positive scalar curvature metric which cannot be extended to a positive scalar curvature metric on $M$ with mean convex…

The discrete Ces\`aro operator $\mathsf{C}$ is investigated in the class of smooth sequence spaces $\lambda_0(A)$ of finite type. This class contains properly the power series spaces of finite type. Of main interest is its spectrum, which…

Elliptic operators on stratified manifolds with any finite number of strata are considered. Under certain assumptions on the symbols of operators, we obtain index formulas, which express index as a sum of indices of elliptic operators on…

In this work we study the spectral zeta function associated with the Laplace operator acting on scalar functions defined on a warped product of manifolds of the type $I\times_{f} N$ where $I$ is an interval of the real line and $N$ is a…

We study operads in unstable global homotopy theory, which is the homotopy theory of spaces with compatible actions by all compact Lie groups. We show that the theory of these operads works remarkably well, as for example it is possible to…

We study the family of operators $\{\mathcal{R}_a\}_{a\in [0,+\infty)}$ associated to the Robin-type problems in a bounded domain $\Omega\subset\mathbb{R}^2$ $$ \begin{cases} -\Delta u = f & \text{in } \Omega, \\ 2 \bar \nu \partial_{\bar…