Generalizations of Sturmian Theory
This chapter is devoted to a brief survey of certain areas to which the Sturmian theory has been extended, and which are intimately related to the subject matter of the preceding chapters. Briefly stated, we shall mention related problems for integro-differential systems, a type of generalized differential equation that in major instances is equivalent to a Riemann-Stieltjes integral equation, quadratic functional theory in Hilbert space due to Hestenes, interrelations with the Weinstein theory of intermediate problems, oscillation theory in the context of a B*-algebra and the topological interpretation of the Sturm theorems in terms of intersection numbers and deformation cycles that has emanated from the 1956 paper of R. Bott .
KeywordsHamiltonian System Boundary Problem Differential System Morse Index Chapter Versus
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