Related papers: Homogeneous operators and homogeneous integral ope…

For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators,…

We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kuersten and the second author. The quantum spaces are chosen such that their coordinate algebras do…

We give a short proof of the fact that each homogeneous linear differential operator $A$ of constant rank admits a homogeneous potential operator $B$, meaning that $\ker A(x)=\mathrm{im\,}B(x)$ for $x\neq 0$. We make some refinements of the…

We interpret homogenousness as a second order property and base it on the same principle as nonmonotonic logic: there might be a small set of exceptions. We use this idea to analyse fundamental questions about defeasible inheritance…

A Hankel operator $\Gamma$ in $L^2(\mathbb{R}_+)$ is an integral operator with the integral kernel of the form $h(t+s)$, where $h$ is known as the kernel function. It is known that $\Gamma$ is positive semi-definite if and only if $h$ is…

We study a homogenization question for stochastic divergence type operator

The Carleman operator is defined as integral operator with kernel $(t+s)^{-1}$ in the space $L^2 ({\Bbb R}_{+}) $. This is the simplest example of a Hankel operator which can be explicitly diagonalized. Here we study a class of self-adjoint…

We develop a framework for multiscale analysis of elliptic operators with high-contrast random coefficients. For a general class of such operators, we provide a detailed spectral analysis of the corresponding homogenised limit operator.…

We consider a class of homogeneous partial differential operators on a finite-dimensional vector space and study their associated heat kernels. The heat kernels for this general class of operators are seen to arise naturally as the limiting…

In many applications involving multi-media data, the definition of similarity between items is integral to several key tasks, e.g., nearest-neighbor retrieval, classification, and recommendation. Data in such regimes typically exhibits…

We discuss various notions generalizing the concept of a homogeneous space to the setting of locally compact quantum groups. On the von Neumann algebra level we find an interesting duality for such objects. A definition of a quantum…

Most real systems consist of a large number of interacting, multi-typed components, while most contemporary researches model them as homogeneous networks, without distinguishing different types of objects and links in the networks.…

We study theoretically the concept of homogenization in optics using an ensemble of randomly distributed resonant stationary atoms with density $\rho$. The ensemble is dense enough for the usual condition for homogenization, viz.…

To construct more homogeneous operators, B. Bagchi and G. Misra in \cite{d} introduced the operator $\left(\begin{smallmatrix} T_0 & T_0-T_1 \\ 0 & T_1\\ \end{smallmatrix}\right)$ and proved that when $T_0$ and $T_1$ are homogeneous…

In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are {\em homogeneous} with respect to the action of the M\"{o}bius group consisting of bi-holomorphic automorphisms of the unit…

We prove that a condition of boundedness of the maximal function of a singular integral operator, that is known to be sufficient for the continuity of the corresponding integral operator in H\"{o}lder spaces, is actually also necessary in…

We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form $(1-<z,w>)^{-\gamma}$ for $\gamma>0$. We find necessary and sufficient conditions for the adjoint of a weighted…

Neural operators are neural network-based surrogate models for approximating solution operators of parametric partial differential equations, enabling efficient many-query computations in science and engineering. Many applications,…

The article $-$ part of a larger thesis which aims to give a detailed description of the generalisation to the category of groups with operators of the classical theory of semisimplicity for modules $-$ presents a straightforward…

We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…