Related papers: A note on perturbation analysis for T-product base…
This preprint is a text for students and teachers on inequalities. Some standard topics are covered on application of calculus to inequality proving. Many examples are considered, stated, solved or partially solved. Some problems are…
Brylawski's tensor product formula expresses the Tutte polynomial of the tensor product of two graphs in terms of Tutte polynomials arising from the tensor factors. Analogous tensor product formulas are known for the ribbon graph polynomial…
We characterize the symmetric measures which satisfy the one dimensional convex infimum convolution inequality of Maurey. For these measures the tensorization argument yields the two level Talagrand's concentration inequalities for their…
We characterize in terms of inequalities the possible generalized singular numbers of a product AB of operators A and B having given generalized singular numbers, in an arbitrary finite von Neumann algebra. We also solve the analogous…
We adopt a new perspective on the tensor product of arbitrary semi-lattices. Our basic construction exploits a description of semi-lattices in terms of bi-extensional Chu spaces associated to a target space defined to be the boolean domain.…
Matrix valued (asymmetric) truncated Toeplitz operators are generally not complex symmetric. In this paper, we define a new conjugation with unique properties and study its relation to matrix valued asymmetric truncated Toeplitz operators.…
We study the perturbation by a critical term and a $(p-1)$-superlinear subcritical nonlinearity of a quasilinear elliptic equation containing a singular potential. By means of variational arguments and a version of the…
We define the tensor product of filtered $A_\infty$-algebras. establish some of its properties and give a partial description of the space of bounding cochains in the tensor product. Furthermore we show that in the case of classical…
We study two classes of linear difference differential equations analogous to Euler-Cauchy ordinary differential equations, but in which multiple arguments are shifted forward or backward by fixed amounts. Special cases of these equations…
Our aim is to introduce the tropical tensor product and investigate its properties. In particular we show its use for solving tropical matrix equations.
In this paper we study the locus of singular tuples of a complex valued multisymmetric tensor. The main problem that we focus on is: given the set of singular tuples of some general tensor, which are all the tensors that admit those same…
We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…
We prove some probabilistic estimates for tensor products of random vectors. As an application we obtain embeddings of certain matrix spaces into $L_1$.
We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions…
The approximation of matrices to the sum of tensor products of Hermitian matrices is studied. A minimum decomposition of matrices on tensor space $H_1\otimes H_2$ in terms of the sum of tensor products of Hermitian matrices on $H_1$ and…
We consider a linearized inverse boundary value problem for the elasticity system. From the linearized Dirichlet-to-Neumann map at zero frequency, we show that a transversely isotropic perturbation of a homogeneous isotropic elastic tensor…
The singular values squared of the random matrix product $Y = G_r G_{r-1} \cdots G_1 (G_0 + A)$, where each $G_j$ is a rectangular standard complex Gaussian matrix while $A$ is non-random, are shown to be a determinantal point process with…
We prove several trace inequalities that extend the Araki Lieb Thirring (ALT) inequality, Golden Thompson (GT) inequality and logarithmic trace inequality to arbitrary many tensors. Our approaches rely on complex interpolation theory as…
This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar…
In this paper we study n-inverse pairs of operators on the tensor product of Banach spaces. In particular we show that an n-inverse pair of elementary tensors of operators on the tensor product of two Banach spaces can arise only from l-…