Results 21 to 30 of about 149,438 (204)

Structure of Finite-Dimensional Protori

Axioms, 2019
A Structure Theorem for Protori is derived for the category of finite-dimensional protori (compact connected abelian groups), which details the interplay between the properties of density, discreteness, torsion, and divisibility within a finite ...
Wayne Lewis
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Straightening Theorem for bounded Abelian groups

Topology and its Applications, 2008
For any abelian group \(G\), let \(G^{\sharp}\) denote the group \(G\) equipped with its Bohr topology, i. e. the initial topology of \(G\) with respect to the family of all homomorphisms of \(G\) into the circle group. For a positive integer \(m\) and a cardinal \(\kappa,\) let \({\mathbb V}_m^{\kappa}=\bigoplus_{\kappa} {\mathbb Z_m},\) where ...
DIKRANJAN, Dikran, DE LEO LORENZO
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Freiman's theorem in an arbitrary abelian group [PDF]

Journal of the London Mathematical Society, 2007
A famous result of Freiman describes the structure of finite sets A of integers with small doubling property. If |A + A| <= K|A| then A is contained within a multidimensional arithmetic progression of dimension d(K) and size f(K)|A|. Here we prove an analogous statement valid for subsets of an arbitrary abelian group.
Green, BJ, Ruzsa, IZ
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Second degree polynomials and the fundamental theorems of harmonic analysis

International Journal of Mathematics and Mathematical Sciences, 1982
The concept of a second degree polynomial with nonzero subdegree is investigated for Abelian groups, and it is shown how such polynomials can be exploited to produce elementary proofs for the Uniqueness Theorem and the Fourier Inversion Theorem in ...
Kelly McKennon
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A Generalization of Arrow’s Lemma on Extending a Binary Relation

International Journal of Mathematics and Mathematical Sciences, 2019
By examining whether the individualistic assumptions used in social choice could be used in the aggregation of individual preferences, Arrow proved a key lemma that generalizes the famous Szpilrajn’s extension theorem and used it to demonstrate the ...
Athanasios Andrikopoulos
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Abelian varieties with isogenous reductions

Comptes Rendus. Mathématique, 2021
Let $A_1$ and $A_2$ be abelian varieties over a number field $K$. We prove that if there exists a non-trivial morphism of abelian varieties between reductions of $A_1$ and $A_2$ at a sufficiently high percentage of primes, then there exists a non-trivial
Khare, Chandrashekhar B., Larsen, Michael   +1 more
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Abelian theorems for Whittaker transforms [PDF]

International Journal of Mathematics and Mathematical Sciences, 1986
Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches 0 or ∞ in absolute value inside a wedge region in the right half plane.
Richard D. Carmichael, R. S. Pathak
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Bundles of generalized theta functions over abelian surfaces [PDF]

, 2016
We study the bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree 0, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors.
Oprea, Dragos
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Ergodic Theorems for Abelian Semi-Groups [PDF]

Transactions of the American Mathematical Society, 1942
Not ...
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Characterisation of Locally Compact Abelian Groups Having Spectral Synthesis

Forum of Mathematics, Sigma
In this paper we solve a long-standing problem which goes back to Laurent Schwartz’s work on mean periodic functions. Namely, we completely characterize those locally compact Abelian groups having spectral synthesis. So far a characterization theorem was
László Székelyhidi
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