Spectral concentration and rapidly decaying potentials
The spectral function \(\rho(\mu)\), \(\mu\geq 0\) for the Sturm-Liouville equation \[ y''+ (\lambda-q)y=0, \qquad q\in L(0,\infty) \] on \([0,\infty)\) is considered with a boundary condition \[ y(0)\cos \alpha+y'(0) \sin\alpha=0. \] A new formula for \(\rho'\) is given and a test for the existence of points of spectral concentration is discussed. (A point is called a point of spectral concentration if \(\rho'\) has a local maximum there.) Computational investigations are given.
scientific article; zbMATH DE number 1043291
scientific article