ABSTRACT

In Chapter 3, we interpreted the term “spectrum” in connection with a multiparameter boundary-value problem as meaning simply the collection of eigenvalues, considered inhomogeneously as k-tuples. We showed there, and in Chapter 5, that under suitable conditions eigenvalues were of finite multiplicity and that the set of eigenvalues had no finite limit-points.The purpose of this chapter is to take account of, so to speak, infinite limit-points of the set of eigenvalues. The treatment will be confined to the non-singular Sturm-Liouville setting of Chapter 3.