6,123,819 A * 9/2000 Peeters ....................... 204/452 6,361,958 B1 * 3/2002 Shieh et al. ................. 435/7.1 6,524,790 B1 * 2/2003 Kopf-Sill et al. .............. 435/6 6,585,939 B1 7/2003 Dapprich 6,599,436 B1 7/2003 Matzke et al. 6,613,512 B1 9/2003 Kopf-Sill et al. 6,649,358 B1 * 11/2003 Parce et al. .................. 435/7.2 6,699,665 B1 * 3/2004 Kim et al. ......................

I consider general reflection coefficients for arbitrary one-dimensional whole line differential or difference operators of order 2. These reflection coefficients are semicontinuous functions of the operator: their absolute value can only go down when limits are taken. This implies a corresponding semicontinuity result for the absolutely continuous spectrum, which applies to a very large class ...

Introduction. In 1923 M. Fekete [2]2 introduced the concept of factor sequences that left invariant the class of a Fourier series. That is, Fekete investigated the conditions to which a sequence of constants (X„) must be subjected in order that (X„a„, X„i„) be Fourier coefficients of a function of the same class, K, as that of the function determined by (an, bn). Whenever (X„) has this property...

While over the last century or more considerable effort has been put into the problem of finding approximate solutions for wave equations in general, and quantum mechanical problems in particular, it appears that as yet relatively little work seems to have been put into the complementary problem of establishing rigourous bounds on the exact solutions. We have in mind either bounds on parametric...