Related papers: A generalization of Forelli's theorem
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…
The Modern Theory of Polarization, which rigorously defines the spontaneous electric polarization of a periodic solid and provides a recipe for its computation in electronic structure codes, transformed our understanding of ferroelectricity…
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
Beginning from the resolution of Dirichlet L function, using the inner product formula of infinite-dimensional vectors in the complex space, the author proved the world's baffling problem--Generalized Riemann hypothesis.
A generalization of L{\"u}roth's theorem expresses that every transcendence degree 1 subfield of the rational function field is a simple extension. In this note we show that a classical proof of this theorem also holds to prove this…
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
We prove a generalization of Frieman's $3k-3$ theorem for the sumset $$ \Sigma^{l}(A_1,\ldots,A_k)=\{a_{j_{1}}+\cdots+a_{j_{l}}:\,1\leq j_{1}<\cdots<j_{l}\leq k,\ a_{j_{s}}\in A_{j_{s}}\text{ for all }s\}. $$
The two parameter generalization of the complete elliptic integral of the second kind discussed recently by Barsan is expressed in terms of ordinary complete elliptic integrals.
The objective of this paper is to describe the structure of Zariski closed algebras, which provide a useful generalization to finite dimensional algebras in the study of representable algebras over finite fields. Our results include a…
The result of this paper is proved in arXiv:1112.1163
In this paper, we reprove a global converse theorem of Cogdell and Piatetski-Shapiro using purely global methods.
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…
It is well known, that Luzin's conjecture has a positive solution for one dimensional trigonometric Fourier series and it is still open for the spherical partial sums $S_\lambda f(x)$, $f\in L_2(\mathbb{T}^N)$, of multiple Fourier series,…
In this short note we have proved an enhanced version of a theorem of Lorentz [1] and its generalization to the multivariate case which gives a non- uniform estimate of degree of approximation by a polynomial with positive coefficients. The…
We provide a new proof of the fractional version of the De Giorgi conjecture for the Allen-Cahn equation in $\mathbb{R}^2$ for the full range of exponents. Our proof combines a method introduced by A. Farina in 2003 with the $s$-harmonic…
In this note, we give a short proof of the Torelli theorem for cubic fourfolds that relies on the global Torelli theorem for irreducible holomorphic symplectic varieties proved by Verbitsky.
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…
In this paper we propose and solve a generalization of the Bernoulli Differential Equation, by means of a generalized fractional derivative. First we prove a generalization of Gronwall's inequality, which is useful for studying the…
In this paper for superparacompact complete metrizable spaces the Freudenthal's theorem for compact irreducible standard polyhedric representation is generalized. Furthermore, for superparacompact metric spaces are reinforced: 1) the…