Abstract
Let Ω be a bounded domain in R d, d>1. It is shown that for every self-adjoint operator M in a separable Hilbert space there exists a self-adjoint realization H of the Laplacian on Ω such that the absolutely continuous part of H is unitarily equivalent to the absolutely continuous part of M. A method to construct H is given.
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References
B. Simon: The Neumann Laplacian of a jelly roll. Proc. Amer. Math. Soc. Vol. 114, No. 3, (1993), 783–785.
R. Hempel, R. Weder: On the completeness of wave operators under loss of local compactness. J. Funct. Analysis 113 (1993), 391–412.
J. F. Brasche: Generalized Schrödinger operators, an inverse problem in spectral analysis and the Efimov effect, pp. 207–245 in S. Albeverio et al. (eds.): Stochastic Processes, Physics and Geometry. World Scientific, Singapore 1989.
J. F. Brasche, H. Neidhardt, J. Weidmann: On the point spectrum of self—adjoint extensions. Math.Zeitschr. 214 (1993),343–355.
J. F. Brasche, H. Neidhardt: On the absolutely continuous spectrum of self—adjoint extensions. Journ. Funct. Analysis 131, (1995), 364–385.
J. F. Brasche, H. Neidhardt: On the singular continuous spectrum of self—adjoint extensions.Math. Zeitschr. 222 (1996), 533–542.
S. Albeverio, J. F. Brasche, H. Neidhardt. On inverse spectral theory for self—adjoint extensions. Journ. Funct. Anal. 154 (1998). 130–173.
J. F. Brasche: On inverse spectral theory for self—adjoint extensions: Nowhere dense singular continuous spectra and Hausdorff dimension of spectra. Preprint of the SFB 237, 1997. Submitted to Journ. Op. Theory.
R. del Rio, S. Jitomirskaya, Y. Last, B. Simon: Operators with singular continuous spectrum IV. Hausdorff dimensions, rank one perturbations, and localization. J. D’Analyse Mathematique 69, 153–200 (1996).
V. A. Derkach, M. M. Malamud: Generalized resolvents and the boundary value problems for Hermitean operators with gap. J. Funct. Analysis 95, (1991), 1–95.
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Brasche, J.F. (1999). On the absolutely continuous energy distribution of a quantum mechanical system in a bounded domain. In: Dittrich, J., Exner, P., Tater, M. (eds) Mathematical Results in Quantum Mechanics. Operator Theory Advances and Applications, vol 108. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8745-8_15
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DOI: https://doi.org/10.1007/978-3-0348-8745-8_15
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