Related papers: The Invariant Subspace Problem
We describe differentiation-invariant subspaces of $C^\infty(a,b)$ which admit spectral synthesis. This gives a complete answer to a question posed by A.~Aleman and B.~Korenblum. It turns out that this problem is related to a classical…
A lower bound for the interleaving distance on persistence vector spaces is given in terms of rank invariants. This offers an alternative proof of the stability of rank invariants.
This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is…
Alon and F\"uredi (European J. Combin. 1993) gave a tight bound for the following hyperplane covering problem: find the minimum number of hyperplanes required to cover all points of the n-dimensional hypercube {0,1}^n except the origin.…
Orbits and bi-invariant subsets of binary $G$-spaces are studied. The problem of the distributivity of a binary action of a group $G$ on a space $X$, which was posed in 2016 by one of the authors, is solved.
We introduce a new decision problem, called Packed Interval Covering (PIC) and show that it is NP-complete.
Problem 540 of J. D. Lawson and M. Mislove in Open Problems in Topology asks whether the process of taking duals terminate after finitely many steps with topologies that are duals of each other. The problem for $T_1$ spaces was already…
We show that Pinney's equation [2] with a constant coefficient can be reduced to its linear part by a simple change of variables. Also, Pinney's original solution is simplified slightly.
A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio. At each iteration, a smaller trace ratio problem is…
Following Beurling's theorem and a study of the topology of invariant subspaces by R. Douglas and C. Pearcy description of path connected components of invariant subspace lattice for shift of multiplicity one has been given by R.Yang. This…
This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems
The results of this paper have been subsumed by the paper "A geometric invariant theory construction of spaces of stable maps," Elizabeth Baldwin and David Swinarski, arXiv:0706.1381
We consider the problem of simultaneously finding lower-dimensional subspace structures in a given $m$-tuple of possibly corrupted, high-dimensional data sets all of the same size. We refer to this problem as simultaneous robust subspace…
In this paper, we will present a new iterative construction for the auxiliary equation of Waring's problem, which seems a little simpler than the one of so called "smooth numbers" in papers [4] and [8], and give same upper bounds of G(k) as…
In this paper two related simplification problems for systems of linear inequalities describing precedence relation systems are considered. Given a precedence relation system, the first problem seeks a minimum subset of the precedence…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
We show that any permutation of ${1,2,...,N}$ can be written as the product of two involutions. As a consequence, any permutation of the elements of an array can be performed in-place in parallel in time O(1). In the case where the…
A time-variant analogue of an interpolation problem equivalent to the relaxed commutant lifting problem is introduced and studied. In a somewhat less general form the problem already appears in the analysis of the set of all solutions to…
We show that irreducible strongly continuous representations of $\mathrm{SL}(2,\mathbb{R})$ on certain Banach spaces are admissible and that the admissibility of Banach space representations of SL(2,R) and the invariant subspace problem are…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…