On the homological and algebraical properties of some Feichtinger algebras

Let G be a locally compact group (not necessarily abelian) and B be a homogeneous Banach space on G, which is in a good situation with respect to a homogeneous function algebra on G. Feichtinger showed that there exists a minimal Banach space B min in the family of all homogenous Banach spaces C on G, containing all elements of B with compact support. In this paper, the amenability and super amenability of B min with respect to the convolution product or with respect to the pointwise product are showed to correspond to amenability, discreteness or finiteness of the group G and conversely. We also prove among other things that B min is a symmetric Segal subalgebra of L 1(G) on an IN-group G, under certain conditions, and we apply our results to study pseudo-amenability and some other homological properties of B min on IN-groups. Furthermore, we determine necessary and sufficient conditions on A under which A min $\mathcal{A}_{\min}$ with the pointwise product is an abstract Segal algebra or Segal algebra in A, whenever A is a homogeneous function algebra with an approximate identity. We apply these results to study amenability of some Feichtinger algebras with respect to the pointwise product.

On the existence of positive solutions for a nonlinear elliptic class of equations in R2 and R3

We study the existence of positive solutions for an elliptic equation in RN for N = 2, 3 which is related with the existence of standing (localized) waves and the existence of the ground state solutions for some physical model or systems in fluid mechanics to describe the evolution of weakly nonlinear water waves. We use a variational approach and the well-known principle of concentration-compactness due to P. Lions to obtain the existence of this type of solutions, even in the case that the nonlinear term g is a non-homogeneous function or an operator defined in H1(RN) with values in R.

Solution of the system of nonlinear PDEs characterizing CES property under quasi-homogeneity conditions

The constant elasticity of substitution (CES for short) is a basic property widely used in some areas of economics that involves a system of second-order nonlinear partial differential equations. One of the most remarkable results in mathematical economics states that under homogeneity condition i.e. the production function is a homogeneous function of a certain degree, there are no other production models with the CES property apart from the famous Cobb–Douglas and Arrow–Chenery–Minhas–Solow production functions. In this paper we generalize this classification result to a much wider framework of production functions under quasi-homogeneity conditions, showing in particular the existence of three new classes of production models with the CES property.

Existence and asymptotic behavior of solutions for a class of semilinear subcritical elliptic systems

In this paper we study the asymptotic behaviour of a family of elliptic systems, as far as the existence of solutions is concerned. We give a special attention to the asymptotic behaviour of W and V as ε goes to zero in the system − ε 2 Δ u + W ( x ) u = Q u ( u , v ) in R N , − ε 2 Δ v + V ( x ) v = Q v ( u , v ) in R N , u , v ∈ H 1 ( R N ) , u ( x ) , v ( x ) > 0 for each x ∈ R N , where ε > 0, W and V are positive potentials of C 2 class and Q is a p-homogeneous function with subcritical growth. We establish the existence of a positive solution by considering two classes of potentials W and V. Our arguments are based on penalization techniques, variational methods and the Moser iteration scheme.

Existence and multiplicity of positive solutions for a critical weight elliptic system in ℝN

In this work, we study the following problem [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are the partial derivatives of the homogeneous function [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].

Cosmological Finsler Spacetimes

Applying the cosmological principle to Finsler spacetimes, we identify the Lie Algebra of symmetry generators of spatially homogeneous and isotropic Finsler geometries, thus generalising Friedmann-Lemaître-Robertson-Walker geometry. In particular, we find the most general spatially homogeneous and isotropic Berwald spacetimes, which are Finsler spacetimes that can be regarded as closest to pseudo-Riemannian geometry. They are defined by a Finsler Lagrangian built from a zero-homogeneous function on the tangent bundle, which encodes the velocity dependence of the Finsler Lagrangian in a very specific way. The obtained cosmological Berwald geometries are candidates for the description of the geometry of the universe, when they are obtained as solutions from a Finsler gravity equation.

Permutations on finite fields with invariant cycle structure on lines

We study the cycle structure of permutations $$F(x)=x+\gamma f(x)$$ F ( x ) = x + γ f ( x ) on $$\mathbb {F}_{q^n}$$ F q n , where $$f :\mathbb {F}_{q^n} \rightarrow \mathbb {F}_q$$ f : F q n → F q . We show that for a 1-homogeneous function f the cycle structure of F can be determined by calculating the cycle structure of certain induced mappings on parallel lines of $$\gamma \mathbb {F}_q$$ γ F q . Using this observation we describe explicitly the cycle structure of two families of permutations over $$\mathbb {F}_{q^2}$$ F q 2 : $$x+\gamma {{\,\mathrm{Tr}\,}}(x^{2q-1})$$ x + γ Tr ( x 2 q - 1 ) , where $$q\equiv -1 \pmod 3$$ q ≡ - 1 ( mod 3 ) and $$\gamma \in \mathbb {F}_{q^2}$$ γ ∈ F q 2 , with $$\gamma ^3=-\frac{1}{27}$$ γ 3 = - 1 27 and $$x+\gamma {{\,\mathrm{Tr}\,}}\left( x^{\frac{2^{2s-1}+3\cdot 2^{s-1}+1}{3}}\right) $$ x + γ Tr x 2 2 s - 1 + 3 · 2 s - 1 + 1 3 , where $$q=2^s$$ q = 2 s , s odd and $$\gamma \in \mathbb {F}_{q^2}$$ γ ∈ F q 2 , with $$\gamma ^{(q+1)/3}=1$$ γ ( q + 1 ) / 3 = 1 .

The Β-Change by Finsler Metric of C-Reducible Finsler Spaces in Finsler Geometry

This paper considered about the β-Change of Finsler metric L given by L*= f(L, β), where f is any positively homogeneous function of degree one in L and β and obtained the β-Change by Finsler metric of C-reducible Finsler spaces. Also further obtained the condition that a C-reducible Finsler space is transformed to a C-reducible Finsler space by a β-change of Finsler metric.