M(\(\lambda\) ) theory for singular Hamiltonian systems with one singular point. (English) Zbl 0683.34008

From the author’s abstract: The theory of singular Hamiltonian systems is developed. Square integrable solutions are exhibited and used to define Green’s function. Using a singular Green’s formula, other self-adjoint boundary value problems are generated in which regular and singular boundary conditions are mixed together. Finally the spectral measure, the generalized Fourier transform of an arbitrary function, and the inverse transform for problems with separated boundary conditions are derived.
Reviewer: A.Boucherif


34B05 Linear boundary value problems for ordinary differential equations
34B20 Weyl theory and its generalizations for ordinary differential equations
34L99 Ordinary differential operators
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