Related papers: A proof of Fatou's interpolation theorem

An technically interesting proof of a known theorem.

We prove that under very mild conditions for any interpolation formula $f(x) = \sum_{\lambda\in \Lambda} f(\lambda)a_\lambda(x) + \sum_{\mu\in M} \hat{f}(\mu)b_{\mu}(x)$ we have a lower bound for the counting functions $n_\Lambda(R_1) +…

We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…

We provide a simple proof of Kamp's theorem.

In this paper, we prove a discrete Rubio de Francia extrapolation theorem via factorization of discrete Muckenhoupt weights and discrete iterated Rubio de Francia algorithm and its duality.

An error bound for Gaussian Interpolation which is better than the current exponential-type error bound is presented.

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary…

We give a new proof of a Fourier interpolation result first proved by Radchenko-Viazovska, deriving it from a vanishing result of the first cohomology of a Fuchsian group with coefficients in the Weil representation.

We give a counterexample of Morrison's cone conjecture for a strict Calabi-Yau threefold.

We give a new simpler proof of a theorem of Jayne and Rogers.

We give a new proof of a version of the main theorem of the previous paper in the series about embedding of an algebraic system into ultraproducts.

We give a geometric description of the interpolating varieties for the algebra of Fourier transforms of distributions (or Beurling ultradistributions) with compact support on the real line.

In recent years important progress has been achieved towards proving the validity of the replica predictions for the (asymptotic) mutual information (or "free energy") in Bayesian inference problems. The proof techniques that have emerged…

D'Alembert made the first serious attempt to prove the Fundamental Theorem of Algebra (FTA) in 1746. An elementary proof of (FTA) based on the same idea is given in Proofs from THE BOOK. We give a shorter and more transperant version of…

We consider the positions of occurrences of a factor $x$ and its binary complement $\overline{x}$ in the Thue-Morse word ${\bf t} = {\tt 01101001} \cdots$, and show that these occurrences are "intertwined" in essentially two different ways.…

Ohno's relation is a well known formula among multiple zeta values. In this paper, we present its interpolation to complex functions.

We prove an improved form of an expectation of Polya and discuss several related questions

This note describes Fatou's lemma and Lebesgue's dominated convergence theorem for a sequence of measures converging weakly to a finite measure and for a sequence of functions whose negative parts are uniformly integrable with respect to…

This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…