Related papers: Controlled scaling of Hilbert space frames for R^2
Frame theory provides a robust method for recovering vectors in a Hilbert space from inner product data, though the associated decomposition formula can be computationally demanding. We relax the frame condition by studying sequences that…
A quadratically constrained quadratic programming problem is considered in a Hilbert space setting, where neither the objective nor the constraint are convex functions. Necessary and sufficient conditions are provided to guarantee that the…
Visual affordance segmentation identifies image regions of an object an agent can interact with. Existing methods re-use and adapt learning-based architectures for semantic segmentation to the affordance segmentation task and evaluate on…
Frame theory is recently an active research area in mathematics, computer science and engineering with many exciting applications in a variety of different fields. This theory has been generalized rapidly and various generalizations of…
We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…
Recent work in Dynamical Sampling has been centered on characterizing frames obtained by the orbit of a vector under a bounded operator. We prove a necessary and sufficient condition for a pair of bounded commuting operators on a separable…
The diagonal in a product of projective spaces is cut out by the ideal of 2x2-minors of a matrix of unknowns. The multigraded Hilbert scheme which classifies its degenerations has a unique Borel-fixed ideal. This Hilbert scheme is generally…
Methods of *-representations in Hilbert space are applied to study of systems of $n$ subspaces in a linear space. It is proved that the problem of description of $n$-transitive subspaces in a finite-dimensional linear space is *-wild for $n…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…
In this paper first we describe all (not necessarily linear or bijective) transformations on $\mathbb{R}^d$ with $2\leq d<\infty$ which preserve the area of parallelograms spanned by any two vectors. We also characterize those (not…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
A classic problem with intriguing implications at the level of both applied differential geometry and theoretical physics is dealt with in this short work: Is there any criterion in order to decide whether a pseudo-Riemannian space can be…
We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our…
We prove that every total sequence in a Hilbert space satisfies the lower frame inequality after scaling. This solves A. Kulikov's "exercise" at mathoverflow.
In this note, we first introduce the notation of weaving cfusion frames in separable Hilbert spaces. After reviewing the conditions for maintaining the weaving c-fusion frames under the bounded linear operator and also, removing vectors…
A definition of frames in Krein spaces is stated and a complete characterization is given by comparing them to frames in the associated Hilbert space. The basic tools of frame theory are described in the formalism of Krein spaces. It is…
Generalizing a definition by Kalra \cite{Kalra}, the purpose of this paper is to analyze cyclic frames in finite-dimensional Hilbert spaces. Cyclic frames form a subclass of the dynamical frames introduced and analyzed in detail by Aldroubi…
Let $\hil$ be a finite dimensional (real or complex) Hilbert space and let $\{a_i\}_{i=1}^\infty$ be a non-increasing sequence of positive numbers. Given a finite sequence of vectors $\f$ in $\hil$ we find necessary and sufficient…
It is shown that the natural framework for the solutions of any Schrodinger equation whose spectrum has a continuous part is the Rigged Hilbert Space rather than just the Hilbert space. The difficulties of using only the Hilbert space to…
The holographic principle suggests that the Hilbert space of quantum gravity is locally finite-dimensional. Motivated by this point-of-view, and its application to the observable Universe, we introduce a set of numerical and conceptual…