Related papers: A note on best n-term approximation for generalize…
Using a local analog of the Wiener-Levi theorem, we investigate the class of measures on Euclidean space with discrete support and spectrum. Also, we find a new sufficient conditions for a discrete set in Euclidean space to be a coherent…
We propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano-Wichmann relations and a representation of the Poincare' group on the one-particle Hilbert space. The abstract real…
In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases.…
This is a short introduction to Hilbert space frame theory and its applications for those outside the area who want to enter the subject. We will emphasize finite frame theory since it is the easiest way to get into the subject.
Recent advances in large-margin classification of data residing in general metric spaces (rather than Hilbert spaces) enable classification under various natural metrics, such as string edit and earthmover distance. A general framework…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions…
We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable…
Kuhn-Tucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions. We propose a class of strongly convergent algorithms for…
We give necessary and sufficient conditions for the sum of n subspaces of a Hilbert space to be closed. We also present various properties of n-tuples of subspaces with closed sum.
\emph{Approximation Theory} uses nicely-behaved subcategories to understand entire categories, just as projective modules are used to approximate arbitrary modules in classical homological algebra. We use set-theoretic \emph{elementary…
We give necessary and sufficient conditions for the embeddings $\Lambda\text{BV}^{(p)}\subseteq \Gamma\text{BV}^{(q_n\uparrow q)}$ and $\Phi\text{BV}\subseteq\text{BV}^{(q_n\uparrow q)}$. As a consequence, a number of results in the…
Recent findings by Jahn, T. Ullrich, Voigtlaender [10] relate non-linear sampling numbers for the square norm to quantities involving trigonometric best $m-$term approximation errors in the uniform norm. Here we establish new results for…
This paper investigates a local central limit theorem for a normalized sequence of random variables belonging to a fixed order Wiener chaos and converging to the standard normal distribution. We prove, without imposing any additional…
We analyze special classes of bi-orthogonal sets of vectors in Hilbert and in Krein spaces, and their relations with generalized Riesz systems. In this way, the notion of the first/second type sequences is introduced and studied. We also…
The aim of this study is to clarify the consequences of recent theoretical results for the numerical computation of expectation by the shift method, and in particular to yield sufficient criteria for the existence of speed of convergence of…
We revisit the fundamental notion of continuity in representation theory, with special attention to the study of quantum physics. After studying the main theorem in the context of representation theory, we draw attention to the significant…
We study the machine learning task for models with operators mapping between the Wasserstein space of probability measures and a space of functions, like e.g. in mean-field games/control problems. Two classes of neural networks, based on…
We derive expressions required in generalizing the Gutzwiller approximation to models comprising arbitrarily degenerate localized orbitals.
In the extended (1 + 4) -dimensional space (T;X,Y,Z,S)-(time-space-interval) it is considered a model joining electromagnetic and gravitational fields. For the equations circumscribing these fields, the exact solutions appropriated to dot…