Related papers: Sampling expansions associated with quaternion dif…
Multidimensional quaternion arrays (often referred to as "quaternion tensors") and their decompositions have recently gained increasing attention in various fields such as color and polarimetric imaging or video processing. Despite this…
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
A novel approach to 3D surface imaging is proposed, allowing for the continuous sampling of 3D surfaces to extract localized perspective transformation coefficients from Fourier spectrum analysis of projected patterns. The mathematical…
A comprehensive analysis of the morphology of the solution space for a special type of quadratic quaternion equation is presented. This equation, which arises in a surface construction problem, incorporates linear terms in a quaternion…
We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is…
A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivation strictly takes into account the laws of…
With view to applications in stochastic analysis and geometry, we introduce a new correspondence for positive definite kernels (p.d.) $K$ and their associated reproducing kernel Hilbert spaces. With this we establish two kinds of…
In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing…
We discuss the relationship between quaternion algebras and quadratic forms with a focus on computational aspects. Our basic motivating problem is to determine if a given algebra of rank 4 over a commutative ring R embeds in the 2x2-matrix…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element, which is then…
Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…
We review the relation between 4n-dimensional quaternion-Kahler metrics with n+1 abelian isometries and superconformal theories of n+1 tensor supermultiplets. As an application we construct the class of eight-dimensional quaternion-Kahler…
We review known factorization results in quaternion matrices. Specifically, we derive the Jordan canonical form, polar decomposition, singular value decomposition, the QR factorization. We prove there is a Schur factorization for commuting…
We develop exact piecewise polynomial sequences on Alfeld splits in any spatial dimension and any polynomial degree. An Alfeld split of a simplex is obtained by connecting the vertices of an $n$-simplex with its barycenter. We show that, on…
The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal…
We solve the problem of Fourier transformation for the one-dimensional $q$-deformed Heisenberg algebra. Starting from a matrix representation of this algebra we observe that momentum and position are unbounded operators in the Hilbert…
In this note semibounded self-adjoint extensions of symmetric operators are investigated with the help of the abstract notion of quasi boundary triples and their Weyl functions. The main purpose is to provide new sufficient conditions on…
We extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian $H$ and its…