Functorial methods in the theory of group representations I

We introduce a candidate for the group algebra of a Hausdorff group which plays the same role as the group algebra of a finite group. It allows to define a natural bijection betweenk-continuous representations of the group in a Hilbert space and continuous representations of the group algebra. Such bijections are known, but to our knowledge only for locally compact groups. We can establish such a bijection for more general groups, namely Hausdorff groups, because we replace integration techniques by functorial methods, i.e., by using a duality functor which lives in certain categories of topological Banach balls (resp., unit balls of Saks spaces).This paper was written while the authors were supported by the Swiss National Science Foundation under grant 21-33644.92.     

Allgemeine Betrachtungen über das Weber'sche Gesetz

Ohne Zusammenfassung     

New Interfaces for Coupling TLC with TOF SIMS

JPC – Journal of Planar Chromatography – Modern TLC - Two interfaces have been tested for coupling thin-layer chromatography (TLC) with time-of-flight secondary-ion mass spectrometry...     

Sub-supersolution method for quasilinear parabolic variational inequalities

This paper is about a systematic attempt to apply the sub-supersolution method to parabolic variational inequalities. We define appropriate concepts of sub-supersolutions and derive existence, comparison, and extremity results for such inequalities.     

Hermitian quadratic eigenvalue problems of restricted rank

We consider a quadratic eigenvalue problem such that the second order term is a Hermitian matrix of rank r, the linear term is the identity matrix, and the constant term is an arbitrary Hermitian matrix . Of the n+r solutions that this problem admits, we show at least n-r to be real and located in specific intervals defined by the eigenvalues of A, whence at most 2r are nonreal occuring in possibly repeated conjugate pairs.     

Gelfand numbers of operators with values in a Hilbert space

In the paper we prove two inequalities involving Gelfand numbers of operators with values in a Hilbert space. The first inequality is a Rademacher version of the main result in [Pa-To-1] which relates the Gelfand numbers of an operator from a Banach spaceX intol ₂ ⁿ with a certain Rademacher average for the dual operator. The second inequality states that the Gelfand numbers of an operatoru froml ₁ ^N into a Hilbert space satisfy the inequality

Linear fractional composition operators on H2

If ? is an analytic function mapping the unit diskD into itself, the composition operatorC _? is the operator onH ² given byC _?f=fo?. The structure of the composition operatorC _? is usually complex, even if the function ? is fairly simple. In this paper, we consider composition operators whose symbol ? is a linear fractional transformation mapping the disk into itself. That is, we will assume throughout that $$\varphi \left( z \right) = \frac{{az + b}}{{cz + d}}$$ for some complex numbersa, b, c, d such that ? maps the unit diskD into itself. For this restricted class of examples, we address some of the basic questions of interest to operator theorists, including the computation of the adjoint.     

The magnetic moment of the 10+ isomer in140Ce andE1 transitions inN=82 isotones caused by outer subshell configurations

Using the reaction¹³⁸Ba(α,2n)¹⁴⁰Ce the magnetic moment of the 10 ₁ ⁺ isomer atE _x =3714.7 keV in theN=82 nucleus¹⁴⁰Ce has been determined by means of the TDPAD method toμ=+10.3(4)μ _N . Measuredg-factors in¹⁴⁰Ce are compared to calculations within the shell model with configuration mixing. For the 10 ₁ ⁺ isomer in¹⁴⁰Ce the four proton configuration π(1g ₇ ^2/2 ,2d ₅ ^2/2 ) has been found to be dominant. From theg-factor measurement strong contributions of multiparticle excitations to thegp2d _3/2,π3s ₁ ² or π1h ₁₁ ² shells and admixtures of neutron excitations to the wave function of the 10 ₁ ⁺ state could be excluded. The strongE1γ-branch of the deexcitation of the 10 ₁ ⁺ isomer in¹⁴⁰Ce can be explained by means of small admixtures of configurations which contain the outer subshell excitationsπ2f _7/2 andπ1h _9/2. On this basisE1 transitions experimentally observed in theN=82 nuclei¹⁴⁰Ce,¹⁴¹Pr and¹⁴⁵Eu may be understood.