On spectral properties of multivalued production mappings in economic dynamics models. (English) Zbl 1513.37056
Summary: Spectral theory of superlinear mappings was created by A.M. Rubinov, who introduced the concepts of eigenvalue and eigenset. He also established the finiteness and discreteness of the spectrum of superlinear mapping, proved the existence of eigencompact and, under some additional conditions, provided a full description of the spectrum. But, in general case, a description of the spectrum of superlinear mapping has not been obtained. This work finishes the construction of above spectral theory and provides a full description of the spectrum of arbitrary normal superlinear mapping.
MSC:
| 37N40 | Dynamical systems in optimization and economics |
| 91B55 | Economic dynamics |
| 47N10 | Applications of operator theory in optimization, convex analysis, mathematical programming, economics |
| 47A06 | Linear relations (multivalued linear operators) |
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