Inversion of Discrete Second-Order Systems

Abstract

Research on these inverse problems began in the Soviet Union, with the work of M.G. Krein. It appears that his primary interest was in the qualitative properties of the solution of, and the inverse problems for, the Sturm-Liouville equation (see Chapter 8), and the discrete problems were studied because such problems were met in any approximate analysis of Sturm-Liouville problems. Krein’s early papers (1933, 1934) concern the theory of Sturm sequences, while the Supplement to Gantmakher and Krein (1950), and Krein (1952) make use of the theory of continued fractions developed by Stieltjes (1918). Krein sees his results as giving mechanical interpretations of Stieltjes’ analysis.

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Pascal’s Pensées