Bounded solutions for 119-01119-01119-01-problem in pseudo-Siegel domains

Summary We study the problem of the existence of bounded solutions for the equation on pseudo-Siegel domains when the data satisfies the condition .

---

Sunto Si studia il problema dell'esistenza di soluzioni limitate per l'equazione sui domini pseudo-Siegel quando il dato soddisfa alla condizione .

---

---

Work done within the Project 40% M.U.R.S.T. «Geometria Reale e Complessa».     

Topological and bornological characterisations of ideals in von Neumann algebras: I

Suppose is a von Neumann algebra on a Hilbert space and is any ideal in . We determine a topology on , for which the members of that are to norm continuous are exactly those in ; and a bornology on such that the elements of which map the unit ball to an element of , equivalently those members of that are norm to bounded, are exactly those in . This is achieved via analogues of the notions of injectivity and surjectivity in the theory of operator ideals on Banach spaces.     

Operator inequalities and construction of Krein spaces

Let be a Hilbert space. A continuous positive operatorT on uniquely determines a Hilbert space which is continuously imbedded in and for which with the canonical imbedding . A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space ( ) which is continuously imbedded in and for which with the canonical imbedding .     

On the tail behaviour of the distribution function of multiple stochastic integrals

Summary Let F _n (u) denote the empirical distribution function of a sample of i.i.d. random variables with uniform distribution on [0, 1]. Define , and consider the integrals where f is a bounded measurable function. We give a good upper bound on the probability . An analogous estimate is given for multiple integrals with respect to a Poisson process.     

Partial regularity of minimizers of quasiconvex integrals with subquadratic growth

We prove partial regularity for minimizers of quasiconvex integrals of the form dx where the integral F() has subquadratic growth, ie .Research supported by MURST, Gruppo Nazionale 40%.     

Laplace approximations for sums of independent random vectors

Summary LetX _i,iN, be i.i.d.B-valued random variables whereB is a real separable Banach space, and a mappingB R. Under some conditions an asymptotic evaluation of is possible, up to a factor (1+o(1)). This also leads to a limit theorem for the appropriately normalized sums under the law transformed by the density exp .     

Change of variables in a multiple integral for local fields

A proof of the formula for locally compact fields andC ¹-isomorphisms :UV, whereU andV are open subsets of , was never published. In this paper we give two short proofs, one of them is a more elementary variant of the other.     

Inequalities of Paley type for noncommutative martingales

Summary The purpose of this paper is to study the validity of the Paley inequality on square function, for noncommutative martingales. Let be a regular gage space, and a sequence of von-Neumann algebras such that we prove that for every , where ɛ_n(F) is the conditional expectation of F with respect to the subalgebra : We also consider the case of a martingale arising in the context of harmonic analysis on noncommutative discrete groups, in analogy to the theorem of R.E.A.C. Paley on Fourier-Walsh series. Entrata in Redazione il 26 gennaio 1977. Partially sponsored by C.N.R.     

A fitting class construction

Summary We present a Fitting Class construction which exploits the properties of a certain class of finite soluble groups of nilpotent length three, called -groups in the paper. In addition we look at a wider class of groups, called in the paper, also of nilpotent length three and examine the question as to what -groups are in .A number of examples are given to illuminate the various classes.The author would like to thank HermannHeineken for supervising his dissertation, from which this paper has sprung, the German Academic Exchange Service (DAAD) for enabling him to study with Prof. Heineken at Universität Würzburg and An Roinn Oideachais for the fellowship which is at present supporting him at University College, Galway.     

Completion of an additive measure to a σ-additive measure by an extension of the space

For an algebra of subsets of a set X there is constructed a set and an algebra of its subsets so that the mapping is a one-to-one correspondence between and and for each additive measure on the measure on defined by the equation is countably additive.Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 71–76, January, 1968.The author wishes to express his deep appreciation to S. V. Fomin, under whose guidance this paper was written.     

Infimal generators and dualities between complete lattices

Summary We give some applications of infimal generators of complete lattices, in the sense of Kutateladze and Rubinov [12], to the study of dualities between two complete lattices E and F (i.e., mappings : E F satisfying for all and all index sets I, including the empty set I=Ø). We give some additional results for E=(2^X, ), F=(2^W, ) and E=(¯R^X, ), F=(¯R^W, ) (where X and W are arbitrary sets), with suitable families of infimal generators. We obtain some lattice- theoretic properties of the relations of [22] between dualities : (2^X, ) (2^W, ), binary relations X×W, polarities (): (2^X, ) (2^W, ), coupling functionals : X×W ¯R and Fenchel-Moreau conjugations c():(¯R^X, ) (¯R^W,).     

On the convergence of powers of interval matrices (2)

Summary Let be a real irreduciblen×n interval matrix. Then a necessary and sufficient condition is given for the sequence of the powers of an interval matrix to converge to a matrix which is not the null matrix. In addition a criterion for is proved to decide whether the limit matrix satisfies the condition of symmetry .     

A modification of the uniqueness criterion for the solution of the Watson problem for a half-plane

It is proved that a known theorem yielding the solution of the Watson problem for a half-plane in terms of the Ostrovskii function remains valid if the Ostrovskii function is replaced by the function 0} r^x /m (x)$$ " align="middle" border="0"> , where for x [n, n+1) the function m(x)=m_n, or by the function .Translated from Matematicheskie Zametki, Vol. 14, No. 5, pp. 609–614, November, 1973.     

Norm-principal bimodules of nest algebras II

Let be a nest in a separably acting factor . We present conditions for a factor to be a bimodule of the nest subalgebraalgß in which is singly generated in the norm topology. Some relevant results about the compact ideal , the quasitriangular algebra and the Calkin algebra are established.This work was supported, in part, by funds provided by the University of North Carolina at Charlotte.     

Entropies with the branching property

Summary It is proved that every entropy with the property of branching has the form , where J is a compositive information measure under a regular binary operation. In particular all the classical entropies with the branching property such as that of Shannon have the form .

---

Sunto Si dimostra che ogni entropia che goda della proprietà di diramazione ha necessariamente la forma dove J è una misura di informazione compositiva con una operazione binaria regolare. In particolare tutte le entropie classiche che godono della proprietà di diramazione quale quella di Shannon hanno la forma .

---

---

Entrata in Redazione il 9 aprile 1973.     

On periodic groups of automorphisms of extremal groups

It is proved that if a periodic group has an extremal normal divisor , determining a complete abelian factor group , then the center of the group contains a complete abelian subgroup , satisfying the relation and intersecting on a finite subgroup. It is also established with the aid of this proposition that every periodic group of automorphisms of an extremal group is a finite extension of a contained in it subgroup of inner automorphisms of the group .Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 91–96, July, 1968.     

Temperature-Dependence of Equilibrium States of a Two-Phase Elastic Medium with the Zero Surface Tension Coefficient

We consider the energy functional of a two-phase elastic medium with quadratic energy densities defined for such that ,where is a measurable characteristic function. Under some natural conditions on the data of the problem, we prove the existence of an interval (t ^-,t ⁺) of the change of temperature such that the energy functional has only a minimizer such that for or such that t^ + $$ " align="middle" border="0"> . The energy functional has no minimizers such that or if . We derive two-sided estimates for the numbers in terms of the characteristics of the two-phase elastic medium and the boundary condition. Bibliography: 3 titles.     

Complétude des métriques lorentziennes de\mathbb{T}^2 et difféomorphismes du cercle

Let and the foliations by the null geodesics of some lorentzian metricg on the torus . We analyse how geodesic completeness properties ofg are related to the dynamics of and .     

Über die Riemannsche Einbettungsgeometrie der Veronesemannigfaltigkeiten

Let E be a n-dimensional euclidean vector space. The subset V _k ⁿ ={x ... x | x E} of ^kE is called a Veronesemanifold. The scalar product of E induces a euclidean structure on ^kE. Passing to the corresponding projective space , one may consider as a riemannian submanifold of the space form . In this paper we study properties of the pair of riemannian manifolds.     

Hankel operators on the weighted Bergman spaces with exponential type weights

Let denote the closed subspace of consisting of analytic functions in the unit disk . For certain class of subharmonic , the Hankel operatorH _b on with symbol is studied. Criteria for boundedness and compactness of such kind of Hankel operators are presented.R. Rochberg's research was partially supported by a grant from the National Science Foundation.