Related papers: Branching Asymptotics on Manifolds with Edge
We study the structure and asymptotic behavior of the resolvent of elliptic cone pseudodifferential operators acting on weighted Sobolev spaces over a compact manifold with boundary. We obtain an asymptotic expansion of the resolvent as the…
We study spectral properties of a class of global infinite order pseudo-differential operators and obtain the asymptotic behaviour of the spectral counting functions of such operators. Unlike their finite order counterparts, their spectral…
A generalization of differential operators are pseudodifferential operators which are used for reasoning about partial differential equations with variable coefficients. A lot of useful properties about classical pseudodifferential…
Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. Relying on a basis of pseudodifferential…
We present the theory of pseudodifferential operators acting on a vector orbibundle over an orbifold, construct the zeta function of an elliptic pseudodifferential operator and show the existence of a meromorphic extension to the complex…
Mixed-norm Lebesgue spaces found their place in the study of some questions in the theory of partial differential equations, as can be seen from recent interest in the continuity of certain classes of pseudodifferential operators on these…
We study properties of pseudodifferential operators which arise in their use in boundary value problems. Smooth domains as well as intersections of smooth domains are considered.
In this article, we explore the boundedness properties of pseudo-differential operators on radial sections of line bundles over the Poincar\'e upper half plane, even when dealing with symbols of limited regularity. We first prove the…
Let $X$ be a compact manifold with boundary. Suppose that the boundary is fibred, $\phi:\pa X\longrightarrow Y,$ and let $x\in\CI(X)$ be a boundary defining function. This data fixes the space of `fibred cusp' vector fields, consisting of…
We introduce two new classes of pseudo-differential operators on open curves. They correspond via a change of variables to subclasses of the periodic pseudo-differential operators, which respectively stabilize even and odd functions. The…
We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in weighted Lebesgue spaces.…
The spectral problem for the high order differential operator with singular weight is considered. If the weight is a generalized derivative of self-similar function with zero spectral degree the asymptotics of eigenvalues is obtained. They…
In this paper we expand on B.-W. Schulze's abstract edge pseudodifferential calculus and introduce a larger class of operators that is modeled on H\"ormander's $\varrho,\delta$ calculus, where $0 \leq \delta < \varrho \leq 1$. This…
We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the limiting probability distribution and the…
We study the low energy resolvent of the Hodge Laplacian on a manifold equipped with a fibred boundary metric. We determine the precise asymptotic behavior of the resolvent as a fibred boundary (aka $\phi$-) pseudodifferential operator when…
Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifold, fractals, graphs ...). Boundedness on $L^p$ for pseudodifferential operators of…
In this paper we study the Besov continuity of pseudo-differential operators on compact homogeneous manifolds $M=G/K.$ We use the global quantization of these operators in terms of the representation theory of compact homogeneous manifolds.
We study the cohomology of the complexes of differential, integral and pseudo forms on odd symplectic manifolds taking the wedge product with the symplectic form as differential. We show that the cohomology classes are in correspondence…
Asymptotic properties of certain arithmetic functions involving exponential divisors are investigated.
We study a linear elliptic differential operator of the form $\mathcal{P}=\Delta + V - \lambda$ on a quasi-asymptotically conical manifold $(M, g)$, where $g$ is a polyhomogeneous metric and $V$ is a $b$-vector field that is unbounded with…