Related papers: A proof of Fatou's interpolation theorem

The goal of this paper is twofold; on one hand we wish to present some statements that can be formulated in terms of Interpolation theory which are equivalent to the truth or the falseness of the Riemann Hypothesis, on the other hand we…

We prove a conjecture by Guo-Niu Han which interpolates between two known hook expansion formulas.

We present an elementary combinatorial proof of the celebrated Friendship theorem. The proof involves looking at independent sets and constructing a bound on their size which forces a contradiction.

We prove that a suitably adjusted version of Peter Jones' formula for interpolation by bounded holomorphic functions gives a sharp upper bound for what is known as the constant of interpolation. We show how this leads to precise and…

We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof…

A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.

In this paper we prove the WALA conjecture.

We prove the Ohno-type relation for the interpolated multiple zeta values, which was introduced first by Yamamoto. Same type results for finite multiple zeta values are also given. Moreover, these relations give the sum formula for…

We prove a generalization of Maehara's lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig's interpolation property. As a…

We obtain another proof of Hermite's integral for the Hurwitz zeta function.

In this article, we prove the following interpolation problem: if the composition of a function and a regular map between affine varieties is a regular function, then there exists a global regular function of the target variety that…

This chapter amalgamates some foundational developments and calculations in factorization homology.

We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable $t$, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in…

We prove some new results related to Tanaka's formula.

The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given.

We will give a simple proof of the ambiguous class number formula.

In this chapter we give a basic overview of known results regarding Craig interpolation for first-order logic as well as for fragments of first-order logic. Our aim is to provide an entry point into the literature on interpolation theorems…

We give a generalization of Fujisawa's theorem in [F]. Our proof of the generalized theorem is purely algebraic and it is simpler than his proof.

The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.

A short and elementary proof is given of a celebrated eigenvalue-perturbation result due to Alfred Brauer.