相关论文: A New Form of Williamson's Product Theorem

Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker W-functions. The integration is performed with respect to the second index, and the first index is…

A version of Jonsson's theorem, as previously generalized, holds in non-modular varieties.

We consider the problem of convergence to zero of matrix products $A_{n}B_{n}\cdots A_{1}B_{1}$ with factors from two sets of matrices, $A_{i}\in\mathscr{A}$ and $B_{i}\in\mathscr{B}$, due to a suitable choice of matrices $\{B_{i}\}$. It is…

We establish a theory of singular Soergel bimodules which is a generalization of (a part of) Williamson's theory. We use a formulation of Soergel bimodules developed by the author.

A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established…

A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.

We show that Wilson's theorem as well as the Wilson quotient can be described by supercongruences modulo any higher prime power involving terms of power sums of Fermat quotients. The new approach uses Bell polynomials and Newton's…

We study Minkowski sums and Hadamard products of algebraic varieties. Specifically we explore when these are varieties and examine their properties in terms of those of the original varieties.

In this paper we obtain a new parametric solution of the problem of finding two triads of biquadrates with equal sums and equal products.

In [8] a notion of generalized Hadamard product was introduced. We show that when certain kinds of tensors interact with the eigenvalues of symmetric matrices the resulting formulae can be nicely expressed using the generalized Hadamard…

In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.

The quintuple product identity are deduced from a new semi-finite form, which are obtained from the very-well-poised $_6\phi_5$ series.

A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose(adjoint). A structure theorem for invertible skew-symmetric operators, which is analogous to the finite…

We give explicit formulas for the intertwinors on the scalar functions over the product of spheres with the natural pseudo-Riemannian product metric using the spectrum generating technique. As a consequence, this provides another proof of…

An analytic proof is proposed of Wiener's theorem on factorization of positive definite matrix-functions.

We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the…

In this paper, we study the doubly warped product manifolds with semisymmetric metric connection. We derive the curvatures formulas for doubly warped product manifold with semi-symmetric metric connection in terms of curvatures of…

A vector variational principle is proved.

A few years ago Fritz Gesztesy raised the issue of whether there was a composition rule for the Witten index analogous to that satisfied by Fredholm operators. In this note we prove a result in this direction and provide an application to…

In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.