Related papers: Convolvability and regularization of distributions
We list multiplier and convolutor spaces of the spaces occurring in L. Schwartz' "Th\'eorie des distributions". Furthermore we clarify whether the multiplications and convolutions are continuous or not.
One can represent Schwartz distributions with values in a vector bundle $E$ by smooth sections of $E$ with distributional coefficients. Moreover, any linear continuous operator which maps $E$-valued distributions to smooth sections of…
This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of…
We prove several Tauberian theorems for regularizing transforms of vector-valued distributions. The regularizing transform of $f$ is given by the integral transform $M^{f}_{\varphi}(x,y)=(f\ast\varphi_{y})(x),$…
We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…
We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to…
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…
We study a well-known problem concerning a random variable $Z$ uniformly distributed between two independent random variables. A new extension has been introduced for this problem and fairly large classes of randomly weighted average…
We investigate regularizations of distributional sections of vector bundles by means of nets of smooth sections that preserve the main regularity properties of the original distributions (singular support, wavefront set, Sobolev…
Set-valued quantiles for multivariate distributions with respect to a general convex cone are introduced which are based on a family of (univariate) distribution functions rather than on the joint distribution function. It is shown that…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
We give necessary and sufficient criteria for a distribution to be smooth or uniformly H\"{o}lder continuous in terms of approximation sequences by smooth functions; in particular, in terms of those arising as regularizations…
We consider distributions on a closed compact manifold $M$ as maps on smoothing operators. Thus spaces of certain maps between $\Psi^{-\infty}(M)\to \mathcal{C}^{\infty}(M)$ are considered as generalized functions. For any collection of…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
The Transformed-Transformer family of distributions are the resulting family of distributions as transformed from a random variable $T$ through another transformer random variable $X$ using a weight function $\omega$ of the cumulative…
We introduce an intrinsic notion of Hoelder-Zygmund regularity for Colombeau generalized functions. In case of embedded distributions belonging to some Zygmund-Hoelder space this is shown to be consistent. The definition is motivated by the…
In this paper, we prove some normality criteria concerning transitivity of normality from one family of meromorphic functions to another which improve and generalize some recent results. We also prove some value distribution results for…
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…
By means of several examples, we motivate that universal properties are the simplest way to solve a given mathematical problem, explaining in this way why they appear everywhere in mathematics. In particular, we present the co-universal…