Asymptotics of polynomials orthogonal with respect to varying measures

Letd be a finite positive Borel measure on the interval [0, 2] such that >0 almost everywhere; andW _n be a sequence of polynomials, degW _n =n, whose zeros (w _n ,1,,w _n,n lie in [|z|1]. Let d _n <> for each_nN, whered _n =d/|W _n (e ⁱ )|². We consider the table of polynomials _n,m such that for each fixednN the system _n,m,mN, is orthonormal with respect tod _n . If

Necessary and sufficient conditions for interpolation with functions having monotoner-th derivatives

,

A class of strongly nonlinear functional differential equations

Let H be a real Hilbert space, :H [0, + ] a proper l.s.c., convex function with L_k:={u H; u² + (u) k} compact for every k > 0, let > 0 be a given constant and . We prove an existence result for strong solutions to a class of functional differential equations of the form

A test of convergence of Fourier series with respect to multiplicative systems,analogous to the Jordan test

, {p _n} _n=0 (p₀=1, _n2 n2). : x f(t) V(G)

On the computation of modules of long quadrilaterals

We study quadrilateralsQ which are given by two intervals on {:Im = 0} and {:Im = 1}, and two Jordan arcs ₁, ₂, in {:0 Im 1} connecting these two intervals. Many practical problems require the determination of the modulem(Q) ofQ, but ifQ is long, i.e., if

Special directions on contact metric three-manifolds

Blair [5] has introduced special directions on a contact metric 3-manifolds with negative sectional curvature for plane sections containing the characteristic vector field and, when is Anosov, compared such directions with the Anosov directions. In this paper we introduce the notion of Anosov-like special directions on a contact metric 3-manifold. Such directions exist, on contact metric manifolds with negative -Ricci curvature, if and only if the torsion is -parallel, namely (1.1) is satisfied. If a contact metric 3-manifold M admits Anosov-like special directions, and is -parallel, where is the Berger-Ebin operator, then is Anosov and the universal covering of M is the Lie group (2,R). We note that the notion of Anosov-like special directions is related to that of conformally Anosow flow introduced in [9] and [14] (see [6]).Supported by funds of the M.U.R.S.T. and of the University of Lecce. 1991.     

Maximal polynomial subordination to univalent functions in the unit disk

Let C be a simply connected domain, 0, and let _n,nN, be the set of all polynomials of degree at mostn. By _n() we denote the subset of polynomials p _n withp(0)=0 andp(D), whereD stands for the unit disk {z: |z|<1}, and=" by=">we denote the maximal range of these polynomials. Letf be a conformal mapping fromD onto ,f(0)=0. The main theme of this note is to relate _n (or some important aspects of it) to the imagesf _s (D), wheref _s (z):=f[(1–s)z], 0s<1. for=" instance=" we=" prove=" the=" existence=" of=" a=" universal=">c ₀ such that, forn2c ₀,     

A note on threefolds with a hyperplane section of general type

This paper deals with polarized pairs , where is a nonsingular projective threefold and is a very ample line bundle on it, such that for one smooth member  | |, one has (Â)=2. A large class of pairs whose adjoint line bundle is nef and big was indirectedly studied by Beltrametti and co-workers. We add some more information, both in this general case and also when the adjoint line bundle fails to be nef and big.     

Special rank two vector bundles over Enriques surfaces

Partially supported by the European Science project Geometry of Algebraic Varieties, Contract SCJ-0398-C(A)     

Some remarks on Turán's inequality. III: The completion

. 0pq, 1–1/p+1/p0. f(x) — n, [–1,1],

Lehmer pairs of zeros,the de Bruijn-Newman constant Λ, and the Riemann Hypothesis

We give here a rigorous formulation for a pair of consecutive simple positive zeros of the functionH ₀ (which is closely related to the Riemann -function) to be a Lehmer pair of zeros ofH ₀. With this formulation, we establish that each such pair of zeros gives a lower bound for the de Bruijn-Newman constant (where the Riemann Hypothesis is equivalent to the assertion that 0). We also numerically obtain the following new lower bound for :

Sharpening of Stečkin's theorem to strong approximation

. . , , : f — ,

Extension of a class of fibered loops to kinematic spaces

The notion of the split extension of a commutative kinematic space is extended to the case of a weak K-loop with an incidence fibration (F, +, ). Theorem 1 states conditions under wich the quasi-direct productG F⁺ _Q with Aut(F, +) can be turned in a fibered incidence group (G, , o) such that (F, +, ) becomes embeddable inG, and Theorem 2 the additional assumption such that (G, , o) is even a kinematic space. In section 4, Theorem 3 shows that there are suitable examples of proper K-loops with an incidence fibration (derived from hyperbolic planes) on which one can apply Theorem 2.Dedicated to Erich Ellers on the occasion of his 70th birthdayResearch supported by M.U.R.S.T. 40% and by C.N.R. (G.N.S.A.G.A.)     

Bruck nets,codes, and characters of loops

Numerous computational examples suggest that if _{k-1 k} are (k- 1)- and k-nets of order n, then rank _{p k} - rank _{p k-1} n - k + 1 for any prime p dividing n at most once. We conjecture that this inequality always holds. Using characters of loops, we verify the conjecture in case k = 3, proving in fact that if p ^e n, then rank _{p 3} 3n - 2 - e, where equality holds if and only if the loop G coordinatizing ₃ has a normal subloop K such that G/K is an elementary abelian group of order p ^e . Furthermore if n is squarefree, then rank _p = 3n - 3 for every prime p ¦ n, if and only if ₃ is cyclic (i.e., ₃ is coordinated by a cyclic group of order n).The validity of our conjectured lower bound would imply that any projective plane of squarefree order, or of order n 2 mod 4, is in fact desarguesian of prime order.     

Blocks of orthogonal random variables and the strong law of large numbers

(X _k ),k=1,2,... — _k ² >1; (X _k ) , E(X _k X _t )=0 p k<>(p+1) (p,k,l=1, 2, ...) , , ,

On the class of an elliptic projective surface

Research done within the framework of the 40% project Algebraic Geometry of the Italian M. U. R. S. T.     

Some notes about affine diameters of convex figures

Given a pointx in a convex figureM, let(x) denote the number of all affine diameters ofM passing throughx. It is shown that, for a convex figureM, the following conditions are equivalent.