Related papers: Modified Green-Hyperbolic Operators
A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics that can be described by the Lindblad master equation in Liouville density operator space. The method extends the Hilbert space…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and…
We consider a class of endomorphisms which contains a set of piecewise partially hyperbolic skew-products with a non-uniformly expanding base map. The aimed transformation preserves a foliation which is almost everywhere uniformly…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
We construct the causal (forward/backward) propagators for the massive Klein-Gordon equation perturbed by a first order operator which decays in space but not necessarily in time. In particular, we obtain global estimates for…
On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the…
Neural operators offer powerful approaches for solving parametric partial differential equations, but extending them to spherical domains remains challenging due to the need to preserve intrinsic geometry while avoiding distortions that…
We suggest a new concept of functional-differential operators with constant delay on geometrical graphs that involves {\it global} delay parameter. Differential operators on graphs model various processes in many areas of science and…
The homogenization of periodic elastic composites is addressed through the reformulation of the local equations of the mechanical problem in a geometric functional setting. This relies on the definition of Hilbert spaces of kinematically…
We define classes of pseudodifferential operators on $G$-bundles with compact base and give a generalized $L^2$ Fredholm theory for invariant operators in these classes in terms of von Neumann's $G$-dimension. We combine this formalism with…
According to Radzikowski's celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of Hadamard form iff they are given by a linear combination of distinguished parametrices…
We describe various ways of obtaining the Hadamard coefficients associated to a normally hyperbolic operator from the corresponding Green's operators. As the Hadamard expansion on its own is not enough for this, we include additional…
For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…
A nonlocal vector calculus was introduced in [2] that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A generalization is developed that provides a more general setting for…
On a suitable class of non-compact manifolds, we study (pseudo)differential operators which feature an asymptotic translation-invariance along one axis and an asymptotic dilation-invariance, or asymptotic homogeneity with respect to…
We introduce a calculus for parameter-dependent singular Green operators on the half-space $\mathbb{R}^n_+$ that combines both elements of Grubb's calculus for boundary value problems of finite regularity and techniques of Schulze's…
We provide a simple proof of dynamical delocalization, that is, time-increasing lower bounds on quantum transport for discrete, one-particle Schrodinger operators on $\ell^2 (\mathbb{Z}^d)$, provided solutions to the Schrodinger equation…
This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention: the first is the possibility of…
The aim of this paper is to establish well-posedness properties for hyperbolic PDEs on Fourier Lebesgue spaces. We consider hyperbolic operators with complex characteristics. Since our approach comes from harmonic analysis, we establish…