Tensor Product Bases and Tensor Diagonals

A Note on Tensor Product of Graphs

Let $G$ and $H$ be graphs. The tensor product $Gotimes H$ of $G$ and $H$ has vertex set $V(Gotimes H)=V(G)times V(H)$ and edge set $E(Gotimes H)={(a,b)(c,d)| acin E(G):: and:: bdin E(H)}$. In this paper, some results on this product are obtained by which it is possible to compute the Wiener and Hyper Wiener indices of $K_n otimes G$.

On tensor product $L$-functions and Langlands functoriality

‎In the spirit of the Langlands proposal on  Beyond Endoscopy ‎we discuss the explicit relation between the Langlands functorial transfers and automorphic $L$-functions‎. ‎It is well-known that the poles of the $L$-functions have deep impact to the Langlands functoriality‎. ‎Our discussion also‎ ‎includes the meaning of the central value of the tensor product $L$-functions in terms of the Langl...

Diagonals in Tensor Products of Operator Algebras

In this paper we give a short, direct proof, using only properties of the Haagerup tensor product, that if an operator algebra A possesses a diagonal in the Haagerup tensor product of A with itself, then A must be isomorphic to a finite dimensional C∗-algebra. Consequently, for operator algebras, the first Hochschild cohomology group, H(A, X) = 0 for every bounded, Banach A-bimodule X , if and ...

Bases and dimensions of bivariate hierarchical tensor-product splines

We prove that the dimension of bivariate tensor–product spline spaces of bi– degree (d, d) with maximum order of smoothness on a multi–cell domain (more precisely, on a set of cells from a tensor–product grid) is equal to the number of tensor–product B–spline basis functions, defined by only single knots in both directions, acting on the considered domain. A certain reasonable assumption on the...

Tensor product multiplicities, canonical bases and totally positive varieties