Related papers: Higher order Schmidt decompositions
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.
Necessary and sufficient conditions for bipartite entanglement are derived, which apply to arbitrary Hilbert spaces. Motivated by the concept of witnesses, optimized entanglement inequalities are formulated solely in terms of arbitrary…
Recently, Andrews and Paule studied Schmidt type partitions using MacMahon's Partition Analysis and obtained various interesting results. In this paper, we focus on the combinatorics of Schmidt type partition theorems and characterize them…
We establish linear profile decompositions for the fourth order Schr\"odinger equation and for certain fourth order perturbations of the Schr\"odinger equation, in dimensions greater than or equal to two. We apply these results to prove…
A necessary and sufficient condition is given for the existence of an embedding of an irreducible subshift of finite type into the Fibonacci-Dyck shift
We obtain bounds for the number of variables required to establish Hasse principles, both for existence of solutions and for asymptotic formulae, for systems of additive equations containing forms of differing degree but also multiple forms…
Our goal is to give Schmidt's subspace theorem for moving hypersurface targets in subgeneral position in projective varieties.
In the work, the property of the second-order subdifferential is studied and second-order optimality conditions are obtained for the minimization problem. We also obtained necessary and sufficient conditions for an extremum for the extremal…
We give necessary and sufficient conditions for differentiating under the integral sign an integral that depends on a parameter. The conditions require the equality of two iterated integrals and depend on being able to integrate every…
Schmidt decomposition is a widely employed tool of quantum theory which plays a key role for distinguishable particles in scenarios such as entanglement characterization, theory of measurement and state purification. Yet, it is held not to…
In this paper, we study multivariate vector sampling expansions on general finitely generated shift-invariant subspaces. Necessary and sufficient conditions for a multivariate vector sampling theorem to hold are given.
Let $\varphi$ be a self-map of the unit disk and let $C_\varphi$ denote the composition operator acting on the standard Dirichlet space $\mathcal{D}$. A necessary condition for compactness of a difference of two bounded composition…
We prove that octants are cover-decomposable into multiple coverings, i.e., for any k there is an m(k) such that any m(k)-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into k…
We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.
We establish both sufficient and necessary conditions for weighted Hardy inequalities in metric spaces in terms of Assouad (co)dimensions. Our sufficient conditions in the case where the complement is thin are new even in Euclidean spaces,…
Necessary and sufficient conditions are given for when a sequence of finite dimensional subspaces (X_n) can be blocked to be a skipped blocking decompositon (SBD). These are very similar to known results about blocking of biorthogonal…
In [7, Papadima and Suciu, When does the associated graded Lie algebra of an arrangement group decompose? Comment. Math. Helv. {\bf 81:4} (2006), 859--875] it is proved that the holonomy Lie algebra of an arrangement of hyperplanes through…
Two homotopy decompositions of supensions of spaces involving polyhedral products are given. The first decomposition is motivated by the decomposition of suspensions of polyhedral products by Bahri, Bendersky, Cohen, and Gitler, and is a…
We study Schmidt rank for a vector (i.e., a pure state) and Schmidt number for a mixed state which are entanglement measures. We show that if a subspace of a certain bipartite system contains no vector of Schmidt rank $\leqslant k$, then…
In this article we extend a euclidean result of David and Semmes to the Heisenberg group by giving a sufficient condition for a $k$-Ahlfors-regular subset to have big pieces of bilipschitz images of subsets of $\R^k$. This Carleson type…