In this paper we consider a nonlinear periodic parabolic boundary value problem with a discontinuous nonmonotone nonlinearity. Using a lifting result for operators of type (S+), a general surjectivity theorem for operators of monotone type and an auxiliary problem defined by truncation and penalization we prove the existence of a solution in the order interval formed by an upper and lower solution. Moreover we show that the set of all such solutions is compact in Lp(T, (Z)).

We prove that the functions of the Bergman spaces Ap on tube domains may be written as Laplace transforms of functions when 1 ≤ p ≤ 2. We give in this context a generalization of the Hausdorff–Young inequality with the exact constant, and deduce from the case p = 2 the expression of the Bergman kernel as a Laplace transform.

We study affine invariants of plane curves from the view point of the singularity theory of smooth functions

The spectrum σ(Tφ) of a Toeplitz operator Tφ on the open unit disc D for a unimodular symbol φ is studied and many sufficient conditions for σ(Tφ)⊆∂D or σ(Tφ) = are given. In particular if φ is a unimodular function in H∞ + C, then σ(Tφ)⊆∂D or σ(Tφ) =

Let α be an automorphism of a free group of rank n. The Scott conjecture, proved by Bestvina-Handel, asserts that the fixed subgroup of α has rank at most n. We give a short alternative proof of this result using R-trees.

Finite groups which are products of pairwise totally permutable subgroups are studied in this paper. The -residual, -projectors and -normalizers in such groups are obtained from the corresponding subgroups of the factor subgroups under suitable hypotheses.

Let Γ be a torsion-free geometrically finite Kleinian group. In this paper, we investigate which systems of loxodromic conjugacy classes of Γ can be simultaneously made parabolic in a group on the boundary of the quasi-conformal deformation space of Γ. We shall prove that for this, it is sufficient that the classes of the system are represented by disjoint primitive simple closed curves on the ideal boundary of H3/Γ.

Provided that the weight function ω satisfies certain submultiplicative and decay conditions, the discrete convolution algebra ℓ1(ω) becomes a commutative radical Banach algebra with identity adjoined. There are obvious closed ideals in ℓ1(ω) and these are denoted standard ideals. Earlier results of Thomas, strengthened by Yakubovich and Domar, showed that if the weight ω is star-shaped then all closed ideals are standard. Consequently, the closed ideal generated by any element f in ℓ1(ω) must be standard.

The requirement that ω be star-shaped (essentially that ω(n)1/n must decrease to zero) is somewhat restrictive in that no local maxima of ω(n)1/n are allowed. We generalize this previous result to apply to the larger class of ε-star shaped weights (0 < ε ≤ 1) which allow such local maxima. If f is a non-zero element on ℓ1(ω) we let the integer α(f) = k0 denote the index of its first non-zero term. We introduce the concept of an ε-peak point for k0. If ε = 1 then ω is star-shaped in the usual sense and there are an infinite number of 1-peak points for any k0. Although this latter fact may fail if 0 < ε < 1, if ω(n)1/n tends to zero sufficiently quickly (dependent on k0 and ε) there will always be an infinite number of ε-peak points for k0.

Our main result is that if ω is an ε-star shaped weight, if f is an non-zero element of ℓ1(ω), if α(f) = k0, and if the number of ε-peak points for k0 is infinite, then the closed ideal generated by f is standard.

Conditions for the existence of solutions of a class of elliptic problems with nonconvex constraints are given in the general framework of pseudo-monotone operators. Applications are considered in unilateral problems of free boundary type, yielding the solvability of a Reynold's lubrication model and of a biological population problem with nonlocal terms and global constraints.

We consider the half linear Sturm-Liouville problem

on the interval [0,1] subject to separated boundary conditions (which may be eigenparameter dependent at x = 1) and use Prüfer techniques to produce an oscillation theory for this problem. Both right definite (r > 0) and left definite (r of both signs) cases are discussed.

We give a necessary and sufficient condition for a sequence {ak}k in the unit ball of ℂn to be interpolating for the class A–∞ of holomorphic functions with polynomial growth. The condition, which goes along the lines of the ones given by Berenstein and Li for some weighted spaces of entire functions and by Amar for H∞ functions in the ball, is given in terms of the derivatives of m ≥ n functions F1, …,Fm ∈ A–∞ vanishing on {ak}k.

For N any member of a large class of finite abelian right centralizer near-rings, the subring of the ring End(N) of endomorphisms of (N, +) generated by the set of right multiplication maps on N is explicitly described as a generalized blocked triangular matrix ring, which in some cases turns out to be a structural matrix ring.

We investigate the behaviour of the classical (non-smooth) Hardy-Littlewood maximal operator in the context of Banach lattices. We are mainly concerned with end-point results for p = ∞. Naturally, the main role is played by the space BMO. We analyze the range of the maximal operator in BMOx. This turns out to depend strongly on the convexity of the Banach lattice . We apply these results to study the behaviour of the commutators associated to the maximal operator. We also consider the parallel results for the maximal fractional integral operator.

We determine the number of conjugacy classes in the natural quotient groups of the Nottingham group over the p-element field up to the quotient of order p3p+1.

Let Gk, n, be the Grassmann manifold consisting in all non-oriented k-dimensional vector subspaces of the space Rk+n. In this paper we will show that any differentiable mapping f: Gk, n → Rm, has infinitely many critical points for suitable choices of the numbers m, n, k.

Let U be the quantized enveloping algebra associated to a simple Lie algebra g by Drinfel'd and Jimbo. Let λ be a classical fundamental weight for g, and ⋯(λ) the irreducible, finite-dimensional type 1 highest weight U-module with highest weight λ. We show that the canonical basis for ⋯(λ) (see Kashiwara [6, §0] and Lusztig [18, 14.4.12]) and the standard monomial basis (see [11, §§2.4 and 2.5]) for ⋯(λ) coincide.

The separating subspace of any Lie derivation on a semisimple Banach algebra A is contained in the centre of A.

We show that if a periodic residually-finite group G has a 2-element with finite centralizer then G is locally finite.

We show that the global dimension, dgA, of every commutative Banach algebra A whose radical is a weighted convolution algebra is strictly greater than one. As an application, we see that in this case H2(A, X) ≠ 0 for some Banach A-bimodule X and thus there exists an unsplittable singular extension of the algebra A.