Related papers: Tight Frame with Hahn and Krawtchouk Polynomials o…
Hilbert space fusion frames are a natural extension of Hilbert space frames, extending the notion from a set of vectors in a Hilbert space to a set of subspaces of a Hilbert space with analogous notions of overcompleteness and boundedness.…
We use functions of a bicomplex variable to unify the existing constructions of harmonic morphisms from a 3-dimensional Euclidean or pseudo-Euclidean space to a Riemannian or Lorentzian surface. This is done by using the notion of…
Ultrafast and accurate physical layer models are essential for designing, optimizing and managing ultra-wideband optical transmission systems. We present a closed-form GN/EGN model, named Polynomial Closed-Form Model (PCFM), improving…
Scalable frames are frames with the property that the frame vectors can be rescaled resulting in tight frames. However, if a frame is not scalable, one has to aim for an approximate procedure. For this, in this paper we introduce three…
We present a scheme to controllably improve the accuracy of tight-binding Hamiltonian matrices derived by projecting the solutions of plane-wave ab initio calculations on atomic orbital basis sets. By systematically increasing the…
We give a simple algorithm for the construction of the tight span of a finite subset of the Manhattan plane.
Finite frames, or spanning sets for finite-dimensional Hilbert spaces, are a ubiquitous tool in signal processing. There has been much recent work on understanding the global structure of collections of finite frames with prescribed…
In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…
In this paper we extend to finite-dimensional Pontryagin spaces the methods used in \cite{CasazzaLeon,Deguang} to build frames from an adjoint and positive operator. It is proved that any frame in finite dimensional Pontryagin space…
A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down…
A frame is a generalization of a basis of a vector space to a redundant overspanning set whose vectors are linearly dependent. Frames find applications in signal processing and quantum information theory. We present a genetic algorithm that…
An equiangular tight frame (ETF) is a type of optimal packing of lines in a real or complex Hilbert space. In the complex case, the existence of an ETF of a given size remains an open problem in many cases. In this paper, we observe that…
The purpose of this paper is to discuss representations of high order $C^0$ finite element spaces on simplicial meshes in any dimension. When computing with high order piecewise polynomials the conditioning of the basis is likely to be…
In an $r$-uniform hypergraph on $n$ vertices a tight Hamilton cycle consists of $n$ edges such that there exists a cyclic ordering of the vertices where the edges correspond to consecutive segments of $r$ vertices. We provide a first…
In this article, we present a constructive method for computing the frame coefficients of finite wavelet frames over prime fields using tools from computational harmonic analysis and group theory.
This paper is concerned with achieving optimal coherence for highly redundant real unit-norm frames. As the redundancy grows, the number of vectors in the frame becomes too large to admit equiangular arrangements. In this case, other…
We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. We present a method to determine the maximum robustness of a frame. We present results on tight subframes and…
Within the framework of finite element systems, we show how spaces of differential forms may be constructed, in such a way that they are equipped with commuting interpolators and contain prescribed functions, and are minimal under these…
This article presents a novel mathematical formalism for advanced manifold--metric pairs, enhancing the frameworks of geometry and topology. We construct various D-dimensional manifolds and their associated metric spaces using functional…
We study tight projective 2-designs in three different settings. In the complex setting, Zauner's conjecture predicts the existence of a tight projective 2-design in every dimension. Pandey, Paulsen, Prakash, and Rahaman recently proposed…