Using properties of an integral transform giving directly the matrix elements of a quantum mechanical operator from the corresponding classical function, we restrict the class of distributions corresponding to bounded operators. As a consequence, we can exhibit a class of functions yielding traceclass operators, and give a bound on their trace-norm.

1 Number Fields 2 1.1 Norm, Trace, and Discriminant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Algebraic Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Dedekind Rings 7 2.1 Fractional Ideals and Unique Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 The Ideal Class Group ...

Many trace elements appear in hair in concentrations related to those in the blood, but the relationship for zinc is complicated by disorders that probably affect its state in the blood. A built-to-order x-ray fluorescence spectrometer was used to measure, nondestructively, the concentrations of 16 elements in a 1-mm interval of a single hair. A scan along a hair strand, together with the known...