The strong convergence of Schrödinger propagators
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- by Alan D. Sloan PDF
- Trans. Amer. Math. Soc. 264 (1981), 557-570 Request permission
Abstract:
Time dependent versions of the Trotter-Kato theorem are discussed using nonstandard analysis. Both standard and nonstandard results are obtained. In particular, it is shown that if a sequence of generators converges in the strong resolvent topology at each time to a limiting generator and if the sequence of generators and limiting generator uniformly satisfy Kisynski type hypotheses then the corresponding Schrodinger propagators converge strongly. The results are used to analyze time dependent, form bounded perturbations of the Laplacian.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 264 (1981), 557-570
- MSC: Primary 47D05; Secondary 03H05, 35B99, 35J10, 81C05
- DOI: https://doi.org/10.1090/S0002-9947-1981-0603781-X
- MathSciNet review: 603781