Related papers: Lax Representations and Zero Curvature Representat…
We study infinite products of reproducing kernels with view to their use in dynamics (of iterated function systems), in harmonic analysis, and in stochastic processes. On the way, we construct a new family of representations of the Cuntz…
We prove an explicit formula for the tensor product with itself of an irreducible complex representation of the symmetric group defined by a rectangle of height two. We also describe part of the decomposition for the tensor product of…
We develop the method for constructing Lax representations of PDEs via the twisted extensions of their algebras of contact symmetries by generalizing the construction to the Lie--Rinehart algebras. We present examples of application of the…
We introduce a nonsymmetric, associative tensor product among representations of Cuntz algebras by using embeddings. We show the decomposition formulae of tensor products for permutative representations explicitly We apply decomposition…
We present a method of determining a Lax representation for similarity reductions of autonomous and non-autonomous partial difference equations. This method may be used to obtain Lax representations that are general enough to provide the…
In this rather brief note we present and discuss techniques for solving Kronecker matrix product least squares problems. Our main contribution is an iterative approach that uses the efficient Kronecker matrix-vector multiplication strategy…
In this paper we consider four basic multidimensional matrix operations (outer product, Kronecker product, contraction, and projection) and two derivative operations (dot and circle products). We start with the interrelations between these…
We investigate several properties of Kronecker (direct, tensor) products of graphs that are planar and $3$-connected (polyhedral, $3$-polytopal). This class of graphs was recently characterised and constructed by the second author [15]. Our…
In this brief note we present a zero-curvature representation for one of the new integrable system found by Mikhailov, Novikov and Wang in nlin.SI/0601046.
We investigate the Lax equation in the context of infinite-dimensional Lie algebras. Explicit solutions are discussed in the sequentially complete asymptotic estimate context, and an integral expansion (sums of iterated Riemann integrals…
The method of contact integrable extensions is used to find new zero-curvature representation for Pleba\~nski's second heavenly equation.
We introduce both the notions of tensor product of convex bodies that contain zero in the interior, and of tensor product of $0$-symmetric convex bodies in Euclidean spaces. We prove that there is a bijection between tensor products of…
The extension of Painlev\'e equations to noncommutative spaces has been considering extensively in the theory of integrable systems and it is also interesting to explore some remarkable aspects of these equations such as Painlev\'e…
We propose a new estimator, the quadratic form estimator, of the Kronecker product model for covariance matrices. We show that this estimator has good properties in the large dimensional case (i.e., the cross-sectional dimension $n$ is…
Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and…
New relations involving curvature components for the various connections appearing in the theory of almost product manifolds are given and the conformal behaviour of these connections are studied. New identities for the irreducible parts of…
Modified Volterra lattice admits two vector generalizations. One of them is studied for the first time. The zero curvature representations, B\"acklund transformations, nonlinear superposition principle and the simplest explicit solutions of…
A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…
In our recent paper [H. Baran, I.S. Krasil'shchik, O.I. Morozov, P. Voj{\v{c}}{\'{a}}k, Symmetry reductions and exact solutions of Lax integrable $3$-dimensional systems, Journal of Nonlinear Mathematical Physics, Vol. 21, No. 4 (December…
We initiate a study of infinite tensor products of projective unitary representations of a discrete group G. Special attention is given to regular representations twisted by 2-cocycles and to projective representations associated with…