Related papers: On Generalizations of the Butterfly Theorem

An erratum to this article is posted at https://gcc.episciences.org/page/errata This paper generalizes results of M. Moon on the fibering of certain compact 3-manifolds over the circle. It also generalizes a theorem of H. B. Griffiths on…

In this paper we show an alternative way of defining Fourier Series and Transform by using the concept of convolution with exponential signals. This approach has the advantage of simplifying proofs of transforms properties and, in our view,…

We generalize some results in Hodge theory to generalized normal crossing varieties.

We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.

The two-sided quaternion Fourier transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization of Beurling's theorem, Hardy, Cowling-Price and Gelfand-Shilov theorems, is obtained for the…

We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums.…

The Titchmarsh convolution theorem is a celebrated result about the support of the convolution of two functions. We present a simple proof based on the canonical factorization theorem for bounded holomorphic functions on the unit disk.

This paper is devoted to the proof Gauss' divergence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently [2] and developed in [4], [5] and [6]. Their peculiarity is…

We give a simple proof of the Fourier Inversion Theorem, using the methods of nonstandard analysis.

In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…

In this note, we describe an interpretation of the (continuous) Fourier transform from the perspective of the Chinese Remainder Theorem. Some related issues, including a new derivation of Poisson summation formula, are discussed.

We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions generated by basic operations involving the Goldman bracket. A…

In this paper under some conditions we generalize a theorem of Harish-Chandra concerning representability of Fourier transforms of orbital integrals.

Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.

We give a characterization of decomposition theory in linear algebra.

In the spirit of the many recent simple models of evolution inspired by statistical physics, we put forward a simple model of the evolution of such models. Like its objects of study, it is (one supposes) in principle testable and capable of…

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.

In this article we survey some recent extensions and generalisations of the celebrated Mass Transference Principle (Beresnevich and Velani, Annals of Mathematics, 2006).

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic…