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Annals of Mathematics, II. Series Vol. 150, No. 3, pp. 10291057 (1999) 

A new approach to inverse spectral theory. I: Fundamental formalismBarry SimonReview from Zentralblatt MATH: The inverse spectral problem of recovering the potential $q(x)$ in the Schrödinger operator $(d^2/dx^2)\allowbreak+q$ on $(0,b)$, with Dirichlet, Neumann or mixedtype boundary condition at $x=b$ if $b$ is finite, from the Weyl $m$function is solved by writing the $m$function in the form $$m(\kappa^2,x)=\kappa\int_0^b A(\alpha,x)e^{2\alpha\kappa} d\alpha +O(e^{(2b\varepsilon)\kappa}),\qquad\kappa\to+\infty,$$ solving the integrodifferential equation $${{ tial A(\alpha,x)}\over{ tial x}}= {{ tial A(\alpha,x)}\over{ tial\alpha}} +\int_0^\alpha A(\beta,x)A(\alpha\beta,x) d\beta,$$ and putting $q(x)=A(0^+,x)$. Smoothness properties of $q$ are related to those of $A$. Known asymptotic results for the Weyl $m$function and Borgtype uniqueness results for the potential are rederived. Reviewed by Cornelis van der Mee Keywords: inverse spectral problem; Weyl $m$function Classification (MSC2000): 34B20 34A55 47E05 34L40 Full text of the article:
Electronic fulltext finalized on: 8 Sep 2001. This page was last modified: 21 Jan 2002.
© 2001 Johns Hopkins University Press
