Statistical experiments and their conical measures

Summary In the theory of functional analytic comparison of statistical experiments (started by L. LeCam) one can characterize equivalence classes of experiments by conical measures (in the sense of G. Choquet). We begin with a short proof of the (known) fact that any conical measure with normed resultant belongs to an experiment class. Then we are concerned with the special case of dominated experiments which are characterized by the extendability of their conical measures to finite concrete measures. These results are in close connection with a paper of E.N. Torgersen (Mixtures and products of dominated experiments. Ann. Statist. 5, 44–64 (1977)).After this we study class properties of experiments which are expressible in terms of their conical measures. Simple examples are domination, existence of bounded densities and compactness. It follows the investigation of a more profound class property which we call extremality and which generalizes the concept of an experiment with a sufficient and boundedly complete subalgebra. Finally we prove that the extreme points of the compact convex set of conical measures with normed resultant are just the conical measures of the extremal experiments.     

Über Eigenwerte und Eigenfunktionen einer Klasse von nichtselbstadjungierten Randwertproblemen

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Über das asymptotische Verhalten von Lösungen der linearen DifferentialgleichungM [y]=λN [y] für groß Werte von |λ|

Ohne Zusammenfassung     

Experimental investigations on gain and maximum output of the He-Ne laser

The influence of homogeneous and inhomogeneous line broadening on gain saturation, optimum decoupling and output power of the He-Ne laser is investigated experimentally. It is shown that both types of broadening are present, and that the output power is essentially determined by the homogeneous part if the gas pressure is chosen for maximum output. Experimental results are obtained forλ=0.633 μ andλ=1.15 μ and tubes of different diameters and lengths.     

Phase-locked ultrashort pulse trains at separate and independently tunable wavelengths

The generation and characterization of femtosecond pulses at three independently tunable visible wavelengths is reported. Selected spectral portions of a common continuum generated in sapphire are amplified in noncollinear optical parametric amplifiers. The phase relation of the pulse trains is analyzed with a nonlinear interferometer based on coherent anti-Stokes Raman scattering and is found to be locked to better than 250 mrad rms. Small spectral shifts of the pulses lead to interference behavior that is consistent with 1 kHz frequency combs.