Homogeneous algebraic varieties defined by Jordan pairs

Every Jordan pair defines an algebraic varietyX containing as a dense open subset.X is projective (affine) if and only if is separable (radical). The Picard group ofX is generated by the irreducible factors of the generic norm of . If is separable then the automorphism group ofX is the projective group of .     

Skew-symmetric derivations of a complex Lie algebra

Let be a complex Lie algebra, its underlying real Lie algebra, a real form of and ·, · the euclidean product induced by the real part of an hermitian inner product on . Let aut be the Lie algebra of skew-symmetric derivations of . We give necessary and sufficient conditions to ensure that aut is composed of skew-hermitian derivations. As an application, we study holomorphy in large subgroups of isometries of Lie groups.     

Chu-Dualität und zwei Klassen maximal fastperiodischer Gruppen

This is a continuation of the paper Zwei Klassen lokalkompakter maximal fastperiodischer Gruppen, [6]. In [6], the classes and were introduced. We give sufficient conditions to conclude thatG is in if one knows thatG/G ₀ is in . If a groupG is in and ifG satisfies the Chu-duality then all closed subgroups ofG satisfy the Chu-duality. The Chu-quasi-dual of the Heisenberg groupH with integral coefficients is computed. It is shown thatH does not satisfy the Chu-duality, thatH is in , and thatH is not in .     

Einige Bemerkungen zum Goldbach'schen Problem

By combinatorial means the authors show the existence of thin sub-sets of primes, useful for Goldbach decompositions. For example, there is a set of primes with , such that all butO(x(ln x)^–A) even integersnx can be written as .

     

On a problem connected with zeros of ζ(s) on the critical line

The existence of zeros ofZ ^(k)(t) in short intervals of the type [T, T+H] is established, whereHT ^a(k)logT, . Hitherto the sharpest bounds for the constanta(k) are obtained by employing a certain exponential averaging technique and the estimation of the relevant exponential sums. Bounds for are also derived, under the assumption that orZ(t) does not vanish in certain short intervals.     

Transvection free groups and invariants of polynomial tensor exterior algebras

Let :GGl(n, ) be a representation of a finite groupG over a field such that the ring of invariants is a polynomial algebra . It is known that in the nonmodular case (i.e., when the order of the group is not divisible by the characteristic of ), the invariants ofG acting on the tensor product of a polynomial and an exterior algebra are given by ,d denoting the exterior derivative. We show that in the modular case, the ring of invariants in is of this form if and only if is a polynomial algebra and all pseudoreflections in (G) are diagonalizable.     

Rings of regular functions on nilpotent orbits and their covers

Summary LetG be a complex semisimple algebraic group with Lie algebra . Let be a nilpotentG-orbit, its ring of regular functions. We derive a formula for as aG-module and prove some partial results on a cover of . We then relate this formula to various existing multiplicity formulas forK-types in Harish-Chandra bimodules ofG.Supported by National Science Foundation Grant DMS-8505550     

Finitely generated relatively universal varieties of Heyting algebras

Given distinct varieties and of the same type, we say that is relatively -universal if there exists an embedding :K from a universal categoryK such that for every pairA, B ofK-objects, a homomorphismf:A B has the formf=_g for someK-morphismg:A B if and only if Im(f) . Finitely generated relatively -universal varieties of Heyting algebras are described for the variety of Boolean algebras, the variety generated by a three element chain, and for the variety generated by the four element Boolean algebra with an added greatest element.Dedicated to the memory of Alan DayPresented by J. Sichler.The support of the NSERC is gratefully acknowledged.     

On a Problem of the Theory of Multiply Local Formations

We describe the -closed n-multiply local formations such that the lattice of all -closed n-multiply local formations between and is Boolean.     

On regularities of the distribution of special sequences

Ifp2 is an integer, then every nonnegative integerk is represented by an expression of the form with integersa _i (k), 0a _i (k)p–1,i=0.1,...,s. The radical-inverse function to the basep, _p (k), is defined by . The sequence is uniformly distributed modulo 1 (it may be called a one-dimensional Halton sequence). In the casep=2 it is the van der Corput sequence. The set of all numbers (0, 1] such that the local discrepancy is bounded inn is determined.     

Functions of translation type and functorial properties of Segal algebras II

In this paper we investigate functorial properties of the Segal algebra which consists of all functionsf in Wiener's algebra onG with Fourier transform in Wiener's algebra on the dual group . Especially may serve as a very large and natural domain for Poisson's formula. Moreover, there is introduced a Segal algebraE ₀(G) containing as a subspace, but still eachfE ₀(S) satisfies Poisson's formula.     

Isometric representations of some quotients ofH ∞ of an annulus

Let denote an annulus,E a finite subset of with at least three elements, and the ideal of functions in which vanish at the points ofE. The quotient does not have a completely isometric representation on a finite dimensional Hilbert space. This complements a result of [11] which implies that the quotient has an isometric representation on a Hilbert space of dimension twice the cardinality ofE.     

Groupwise density and related cardinals

We prove several theorems about the cardinal associated with groupwise density. With respect to a natural ordering of families of nond-ecreasing maps from to, all families of size are below all unbounded families. With respect to a natural ordering of filters on, all filters generated by sets are below all non-feeble filters. If then and . (The definitions of these cardinals are recalled in the introduction.) Finally, some consequences deduced from by Laflamme are shown to be equivalent to .     

On a class of operators with finiterank self-commutators

This paper studies the class of pure operatorsA on a Hilbert space satisfying dimK _A <, where . The main tool is a pair of matrices and . A reproducing kernel Hilbert space model is introduced for a subclass of this class of operators. Some theorems are established for some subnormal operators as well as hyponormal operators in this class.     

Lattice invariant valuations on rational polytopes

Let be a lattice ind-dimensional euclidean space , and the rational vector space it generates. If is a valuation invariant under, andP is a polytope with vertices in , then for non-negative integersn there is an expression , where the coefficient(P, n) depends only on the congruence class ofn modulo the smallest positive integerk such that the affine hull of eachr-face ofk P is spanned by points of. Moreover, _r satisfies the Euler-type relation where the sum extends over all non-empty facesF ofP. The proof involves a specific representation of simple such valuations, analogous to Hadwiger's representation of weakly continuous valuations on alld-polytopes. An example of particular interest is the lattice-point enumeratorG, whereG(P) = card(P); the results of this paper confirm conjectures of Ehrhart concerningG.     

A Remark on Subgroup Separability in the Class of Finite π-Groups

We prove that if a group G is residually , then for every -subgroup of the group G, the set of -roots from this subgroup is a -separable -subgroup.     

A representation theorem for weak automorphisms of a universal algebra

Given a group G and a descending chainG ₀,G ₁,...,G _n, of normal subgroups ofG, we prove that there exists a universal algebra , such that the chain ...W_n( )...W₁( }) W₀( )W( ) is isomorphic to the chain ...G _n ...G ₁G ₀G, where W( ) is the group of weak automorphisms of , and W_n( ) is the group of weak automorphisms of that leaves alln-ary operations fixed.We also prove that there are an infinite number of non-isomorphic algebras that satisfy the above.These results are a generalization of those proved by J. Sichler, in the special case when G=G₀, and G₁=G₂=...=G_n=....Presented by J. Mycielski.This paper comprises part of the author's doctoral dissertation at the University of Notre Dame in 1983. The author wishes to express her deep gratitude to Professor Abraham Goetz for suggesting this problem, for being extremely generous with his time and experience, and for giving her his constant encouragement. The author also thanks the reviewer for his helpful comments.     

Common invariant subspaces for collections of operators

Let be a collection of bounded operators on a Banach spaceX of dimension at least two. We say that is finitely quasinilpotent at a vectorx ₀X whenever for any finite subset of the joint spectral radius of atx ₀ is equal 0. If such collection contains a non-zero compact operator, then and its commutant have a common non-trivial invariant, subspace. If in addition, is a collection of positive operators on a Banach lattice, then has a common non-trivial closed ideal. This result and a recent remarkable theorem of Turovskii imply the following extension of the famous result of de Pagter to semigroups. Let be a multiplicative semigroup of quasinilpotent compact positive operators on a Banach lattice of dimension at least two. Then has a common non-trivial invariant closed ideal.This work was supported by the Research Ministry of Slovenia.     

Semilinear hyperbolic systems and equations with singular initial data

We study the weak limits (t, .)of solutions to semilinear strictly hyperbolic systems and wave equations with initial datau (0, .) approximating a distribution, 0 < 1. We propose an optimal link between the singularity of and the growth of the nonlinear term in order that exists. In this way we extend some of the results in [3], [10], [13].     

Zur Interpolation und Integration differenzierbarer periodischer Funktionen

Summary Letx ₀<x ₁<...<x _n–1<x ₀+2 be nodes having multiplicitiesv ₀,...,v _n–1, 1v _k r (0k<n). We approximate the evaluation functional ,x fixed, and the integral respectively by linear functionals of the form and determine optimal weights for the Favard classesW _r C ₂. In the even case of optimal interpolation these weights are unique except forr=1,x(x _k +x _k–1)/2 mod 2. Moreover we get periodic polynomial splinesw _{k, j} (0k<n, 0j<v _k ) of orderr such that are the optimal weights. Certain optimal quadrature formulas are shown to be of interpolatory type with respect to these splines. For the odd case of optimal interpolation we merely have obtained a partial solution.

Bojanov hat in [4, 5] ähnliche Resultate wie wir erzielt. Um Wiederholungen zu vermeiden, werden Resultate, deren Beweise man bereits in [4, 5] findet, nur zitiert