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- W2952803495 abstract "We continue the study of the A-amplitude associated to a half-line Schrodinger operator, -d^2/dx^2+ q in L^2 ((0,b)), b 0. We discuss five issues here. First, we extend the theory to general q in L^1 ((0,a)) for all a, including q's which are limit circle at infinity. Second, we prove the following relation between the A-amplitude and the spectral measure rho: A(alpha) = -2int_{-infty}^infty lambda^{-frac12} sin (2alpha sqrt{lambda}), drho(lambda) (since the integral is divergent, this formula has to be properly interpreted). Third, we provide a Laplace transform representation for m without error term in the case b<infty. Fourth, we discuss m-functions associated to other boundary conditions than the Dirichlet boundary conditions associated to the principal Weyl-Titchmarsh m-function. Finally, we discuss some examples where one can compute A exactly." @default.
- W2952803495 created "2019-06-27" @default.
- W2952803495 creator A5038838154 @default.
- W2952803495 creator A5053434924 @default.
- W2952803495 date "1998-09-29" @default.
- W2952803495 modified "2023-09-27" @default.
- W2952803495 title "A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure" @default.
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- W2952803495 hasPublicationYear "1998" @default.
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