January 1941
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9 Reads
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130 Citations
American Journal of Mathematics
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... We also derive an interesting interpretation (as periodicity of characteristic billiard or the John's mapping) of the Fredholm's property violation. For second-order hyperbolic equations, the fact that periodicity of the John's algorithm is sufficient for violation of the Fredholm property for the Dirichlet problem was proved by John [15] (for the wave equation) and Burskii and Zhedanov [3] (for general second-order hyperbolic equations with constant complex coefficients). Analogous result is true for fourth-order hyperbolic equations and will be proved in the present study. ...
- Citing Article
January 1941
American Journal of Mathematics