相关论文: Decomposition of spaces of distributions induced b…

Considering functions $ f $ on $ \R^n $ for which both $ f $ and $ \hat{f} $ are bounded by the Gaussian $ e^{-{1/2}a|x|^2}, 0 < a < 1 $ we show that their Fourier-Hermite coefficients have exponential decay. Optimal decay is obtained for $…

We characterize bounded, compact, and Hilbert-Schmidt composition-differentiation operators on weighted Dirichlet spaces. The essential norm is estimated via the asymptotic behavior of a function that involves the generalized Nevanlinna…

We construct and investigate the properties of tempered ultradistribution spaces in Sobolev spaces. A new Sobolev space preserving the original properties and condition whose derivatives are linear continuous operators embedding in $L^p$…

Entanglement of bipartite squeezed states generated by holomorphic Hermite functions of two complex variables is investigated using phase-space approach based on the Wigner distribution function. Orthogonality of the holomorphic Hermite…

Following a recent work in which it is shown that a spacetime admitting Lie-group actions may be disjointly decomposed into a a closed subset with no interior plus a dense finite union of open sets in each of which the character and…

We use the author's previous work on atomic decompositions of Besov spaces with spectrum on symmetric cones, to derive new atomic decompositions for Bergman spaces on tube type domains. It is related to work by Ricci and Taibleson who…

We give a motivated introduction to the theory of perverse sheaves, culminating in the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the theory develops naturally from classical…

Recently Stephen Theriault and I found an elementary construction of Anick's spaces and proved their main properties(arXiv:0710.1024).In this work the fundamental fibration is decomposed. This is useful in studying maps out of Anick's…

We introduce an interesting method of proving separable reduction theorems - the method of elementary submodels. We are studying whether it is true that a set (function) has given property if and only if it has this property with respect to…

We show that, for Finsler spaces with cubic metric, Landsberg spaces are Berwaldian. Also, for decomposable metrics, we determine specific conditions for a space with cubic metric to be of Berwald type, thus refining the result in [6].

In these notes we give a brief introduction to decomposition theory and we summarize some classical and well-known results. The main question is that if a partitioning of a topological space (in other words a decomposition) is given, then…

In this paper, we establish the equivalence between the Haj{\l}asz-Sobolev spaces or classical Triebel-Lizorkin spaces and a class of grand Triebel-Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and…

In 1920s R. L. Moore introduced \emph{upper semicontinuous} and \emph{lower semicontinuous} decompositions in studying decomposition spaces. Upper semicontinuous decompositions were studied very well by himself and later by R.H. Bing in…

We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system"…

We extend the Hairer reconstruction theorem for distributions due to Caravenna and Zambotti (arXiv:2005.09287) to general function spaces satisfying a translation and scaling condition. This includes Besov type spaces with exponents below 1…

We continue the study of the variable exponent Morreyfied Triebel-Lizorkin spaces introduced in a previous paper. Here we give characterizations by means of atoms and molecules. We also show that in some cases the number of zero moments…

On a metric measure space satisfying the doubling property, we establish several optimal characterizations of Besov and Triebel-Lizorkin spaces, including a pointwise characterization. Moreover, we discuss their (non)triviality under a…

In this paper we introduce new function spaces which we call anisotropic hyperbolic Besov and Triebel-Lizorkin spaces. Their definition is based on a hyperbolic Littlewood-Paley analysis involving an anisotropy vector only occurring in the…

It is known for decades that computer-based systems cannot be understood without a concept of modularization and decomposition. We suggest a universal, expressive, intuitively attractive composition operator for Petri nets, combined with a…

We consider the deformations of Whitham systems including the "dispersion terms" and having the form of Dubrovin-Zhang deformations of Frobenius manifolds. The procedure is connected with B.A. Dubrovin problem of deformations of Frobenius…