For a point set in the multidimensional unit torus we introduce an Lk-measure of uniformity of distribution, which for k=2 reduces to diaphony (and thus in this case essentially coincides with Weyl L2-discrepancy). For k ∈ [1, 2] we establish a sharp asymptotic for this new measure as the number of points of the set tends to infinity. Upper and lower-bound estimates are given also for k >2.

Let f be a transcendental entire function and denote the n-th iterate fn. For n ≥ 2, we give an explict estimate of the number of periodic points of f with period n, that is, fix-points of fn which are not fix-points of fk for 1 ≤ k <n.

In this paper we describe the moduli spaces of degree d branched superminimal immersions of a compact Riemann surface of genus g into S4. We prove that when d ≥ max {2g, g + 2}, such spaces have the structure of projectivzed fibre products and are path-connected quasi projective varieties of dimension 2d − g + 4. This generalizes known results for spaces of harmonic 2-spheres in S4.

This paper gives non-embeddings and non-immersions for the real flag manifolds RF(1, 1, n–2), n > 3 and shows that Lam's immersions for n = 4 and 5 and Stong's result for n = 6 are the best possible.

In this paper we show that, for analytic composition operators between weighted Bergman spaces (including Hardy spaces) and as far as boundedness, compactness, order boundedness and certain summing properties of the adjoint are concerned, it is possible to modify domain spaces in a systematic fashion: there is a space of analytic functions which embeds continuously into each of the spaces under consideration and on which the above properties of the operator are decided.

A remarkable consequence is that, in the setting of composition operators between weighted Bergman spaces, the properties in question can be identified as properties of the operator as a map between appropriately chosen Hilbert spaces.

We define the Radon transform for functions on the set of chambers of affine, locally finite, rank three buildings. We investigate the problem of the inversion of this transform. Explicit inversion formulas are exhibited for functions which fulfill required summability conditions.

We consider positive linear operators of probabilistic type L1f acting on real functions f defined on the positive semi-axis. We deal with the problem of uniform convergence of L1f to f, both in the usual sup-norm and in a uniform Lp type of norm. In both cases, we obtain direct and converse inequalities in terms of a suitable weighted first modulus of smoothness of f. These results are applied to the Baskakov operator and to a gamma operator connected with real Laplace transforms, Poisson mixtures and Weyl fractional derivatives of Laplace transforms.

Suppose that G is a π-separable group. Let N be a normal π1-subgroup of G and let H be a Hall π-subgroup of G. In this paper, we prove that there is a canonical basis of the complex space of the class functions of G which vanish of G-conjugates ofHN. When N = 1 and π is the complement of a prime p, these bases are the projective indecomposable characters and set of irreduciblt Brauer charcters of G.

In this paper we extend a theorem of Mallet-Paret and Sell for the existence of an inertial manifold for a scalar-valued reaction diffusion equation to new physical domains ωn ⊂ Rn, n = 2,3. For their result the Principle of Spatial Averaging (PSA), which certain domains may possess, plays a key role for the existence of an inertial manifold. Instead of the PSA, we define a weaker PSA and prove that the domains φn with appropriate boundary conditions for the Laplace operator, δ, satisfy a weaker PSA. This weaker PSA is enough to ensure the existence of an inertial manifold for a specific class of scalar-valued reaction diffusion equations on each domain ωn under suitable conditions.