Wehlau, David L.
Published in
Forum Mathematicum

We consider a Weitzenböck derivation Δ acting on a polynomial ring R=K[ξ 1 ,ξ 2 ,...,ξ m ]$ R=K[\xi _1,\xi _2,\ldots ,\xi _m] $ over a field K of characteristic 0. The K-algebra R Δ ={h∈R∣Δ(h)=0}${R^\Delta = \lbrace h \in R \mid \Delta (h) = 0\rbrace }$ is called the algebra of constants. Nowicki considered the case where the Jordan matrix for Δ ac...

Dikranjan, Dikran Martín-Peinador, Elena Tarieladze, Vaja
Published in
Forum Mathematicum

For a topological abelian group X we topologize the group c 0 (X)$c_0(X)$ of all X-valued null sequences in a way such that when X=ℝ${X={\mathbb {R}}}$ the topology of c 0 (ℝ)$c_0({\mathbb {R}})$ coincides with the usual Banach space topology of the classical Banach space c0. If X is a non-trivial compact connected metrizable group, we prove that c...

Śliwa, Wiesław
Published in
Forum Mathematicum

A complete valued field (K,|·|)$(K, |\cdot |)$ is non-archimedean if its valuation satisfies the strong triangle inequality |a+b|≤max{|a|,|b|}$|a+b|\le \max \lbrace |a|, |b|\rbrace $ for all a,b∈K$a,b \in K$ . We say that a pair (E,F) of Fréchet spaces over a non-archimedean field 𝕂 is splitting if for every Fréchet space G over 𝕂 and for every clo...

Al-Ali Bani Ata, Mashhour I. Al-Shemas, Eman
Published in
Forum Mathematicum

The aim of this paper is to show that there is no semifield of order q8, q an odd prime, over 𝔽q, which admits an elementary abelian 2-group E ≅ 23 of automorphisms.

Hu, Guoen Meng, Yan Yang, Dachun
Published in
Forum Mathematicum

Let (𝒳,d,μ)$({\mathcal {X}},d,\mu )$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. Under this assumption, the authors establish some weighted norm inequalities for the multilinear Calderón–Zygmund operators via first obtaining some weighted estimates involving the John–Strömbe...

Quadrelli, Claudio
Published in
Forum Mathematicum

A Bloch–Kato pro-p group G is a pro-p group with the property that the 𝔽 p $\mathbb {F}_p$ -cohomology ring of every closed subgroup of G is quadratic. It is shown that either such a pro-p group G contains no closed free pro-p groups of infinite rank, or there exists an orientation θ:G→ℤ p × $\theta \colon G\rightarrow \mathbb {Z}_p^\times $ such t...

Dos Santos Ferreira, David Kenig, Carlos E. Salo, Mikko
Published in
Forum Mathematicum

In this article we prove Lp estimates for resolvents of Laplace–Beltrami operators on compact Riemannian manifolds, generalizing results of Kenig, Ruiz and Sogge (1987) in the Euclidean case and Shen (2001) for the torus. We follow Sogge (1988) and construct Hadamard's parametrix, then use classical boundedness results on integral operators with os...

Xiong, Bao-Lin Zhang, Pu Zhang, Yue-Hui
Published in
Forum Mathematicum

We generalize Ringel and Schmidmeier's theory on the Auslander–Reiten translation of the submodule category 𝒮 2 (A)$\mathcal {S}_2(A)$ to the monomorphism category 𝒮 n (A)$\mathcal {S}_n(A)$ ; the category consists of all chains of (n-1)$(n-1)$ composable monomorphisms of A-modules. As in the case of n=2$n=2$ , 𝒮 n (A)$\mathcal {S}_n(A)$ has Auslan...

Kohnen, Winfried Martin, Yves
Published in
Forum Mathematicum

We characterize all cusp forms among the degree two Siegel modular forms by the growth of their Fourier coefficients. We also give a similar result for Jacobi forms over the group SL 2 (ℤ)⋉ℤ 2 $\mathrm {SL}_{2}(\mathbb {Z}) \ltimes \mathbb {Z}^2$ .

Albrecht, Ulrich Breaz, Simion Schultz, Phill
Published in
Forum Mathematicum

The aim of this paper is to investigate the relationship between the Abelian groups G with Ext(G,G (κ) )=0${\operatorname{Ext}(G,G^{(\kappa )}) = 0}$ and those satisfying Ext(G,G (κ) )≅Ext(G,G) (κ) ${\operatorname{Ext}(G,G^{(\kappa )})\cong \operatorname{Ext}(G,G)^{(\kappa )}}$ for various cardinals κ. In particular, we will give the structure of s...