Generalizations of Cauchy’s summation theorem for Schur functions

Summation formulas for Schur functions involving hyperdeterminants

We give general integral formulas involving for hyperdeterminants or hyperpfaffians. In the applications, we obtain several summation formulas for the products of Schur functions, which are generalizations of Cauchy’s determinant. Further, we study Toeplitz hyperdeterminants by using the theory of Jack polynomials and give a hyperdeterminant version of a strong Szegö limit theorem. MSC-class: p...

Titchmarsh theorem for Jacobi Dini-Lipshitz functions

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

Generalizations of some irreducibility results by Schur

A Theorem and a Conjecture on Rectangles and Schur Functions

Fix a rectangular Young diagram R, and consider all the products of Schur functions sλsλc , where λ and λ c run over all (unordered) pairs of partitions which are complementary with respect to R. Theorem: The self-complementary products, s λ where λ = λ, are linearly independent of all other sλsλc . Conjecture: The products sλsλc are all linearly independent.

Generalizations of Hedberg's Theorem

As the groupoid interpretation by Hofmann and Streicher shows, uniqueness of identity proofs (UIP) is not provable. Generalizing a theorem by Hedberg, we give new characterizations of types that satisfy UIP. It turns out to be natural in this context to consider constant endofunctions. For such a function, we can look at the type of its fixed points. We show that this type has at most one eleme...