Related papers: Microlocal analysis in generalized function algebr…
Let $\mathcal{M}\subseteq\mathcal{B}\left( \mathcal{H}\right) $ be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weight $\tau$ where $\mathcal{B}\left( \mathcal{H}\right) $ is the…
We discuss the concept of a mesoscopic wavefunction, first in a general context, as the concept of wavefunction has evolved, and then in a more specific context of modeling. The paper concentrates on a simple, abstract one-dimensional…
We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalized) distribution theoretic result on operators with smooth…
An action of a Lie algebra $\frak g$ on a manifold $M$ is just a Lie algebra homomorphism $\zeta:\frak g\to \frak X(M)$. We define orbits for such an action. In general the space of orbits $M/\frak g$ is not a manifold and even has a bad…
Let G be a locally compact non-compact group. We show that under a very mild assumption on the weight function w, the weighted group algebra L_1(G,w) is strongly Arens irregular in the sense of Dales-Lamb-Lau. To this end, we first derive a…
We present a theory for splitting algebras of monic polynomials over rings, and apply the results to symmetric functions, and Galois theory. Our main result is that the ring of invariants of a splitting algebra under the symmetric group…
We study the topological duals of the Colombeau algebras $\Gc(\Om)$, $\G(\Om)$ and $\GS(\R^n)$, discussing some continuous embeddings and the properties of generalized delta functionals.
A local existence and uniqueness theorem for ODEs in the special algebra of generalized functions is established, as well as versions including parameters and dependence on initial values in the generalized sense. Finally, a Frobenius…
The purpose of this contribution is to give a coherent account of a particular narrative which links locales, geometric theories, sheaf semantics and constructive commutative algebra. We are hoping to convey a firm grasp of three ideas: (1)…
We use the framework of Colombeau algebras of generalized functions to study existence and uniqueness of global generalized solutions to mixed non-local problems for a semilinear hyperbolic system. Coefficients of the system as well as…
It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations…
Let L^1(G) and M(G) be group algebra and measure algebra of a locally compact group G, respectively and D:L^1(G)-->M(G) be a continuous linear map. We consider D behaving like derivation or anti-derivation at orthogonal elements for several…
We study the globalization of partial actions on sets and topological spaces and of partial coactions on algebras by applying the general theory of globalization for geometric partial comodules, as previously developed by the authors. We…
Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…
We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…
We develop a systematic approach for resolving the analytic wave front set for a class of integral geometry transforms appearing in various tomography problems. Combined with microlocal analytic continuation, this leads to uniqueness and…
We introduce the notion of an introverted Boolean algebra $\cal B$ of closed-and-open subsets of a topological group $G$, show that the associated Stone space $(\nu_{\cal B} G, \nu_{\cal B})$ is a totally disconnected semigroup…
The local trace function introduced in \cite{Dut} is used to derive equations that relate multiwavelets and multiscaling functions in the context of a generalized multiresolution analysis, without appealing to filters. A construction of…
In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…
This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoelliptic operators, with homogeneous multi-point time-nonlocal…