The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Functional Analysis

  • Leonid Kantorovich
  • Victor Polterovich
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_1098

Abstract

A branch of mathematics mainly concerned with infinite-dimensional vector spaces and their maps, functional analysis is so called because elements (points) of certain important specific spaces are functions. The necessity of considering infinite-dimensional models arises in economics in many problems, including assessment of random effects in a situation with an infinite number of natural states; study of effects arising from a ‘very large’ number of participants; problems of spatial economics; study of economic development in continuous time, in particular, with due regard for lags; economic growth on an infinite time interval; and the influence of commodity differentiation on exchange processes.

Keywords

Competition models Competitive equilibrium Economic growth in the very long run Extension principle Fixed-point theorems Functional analysis Global analysis Hyperplanes Infinite-dimensional models Kakutani theorem Mathematical economics Measure theory Monopolistic competition Openness principle Product differentiation Separation theorems Spatial economics Spectral analysis Uniform boundedness principle 
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Bibliography

  1. Dunford, N., and J.T. Schwartz. 1958. Linear operators. New York: Interscience Publishers.Google Scholar
  2. Ekeland, I., and R. Temam. 1976. Convex analysis and variational problems, Studies in mathematics and its applications. Vol. 1. Amsterdam: North-Holland.Google Scholar
  3. Hildenbrand, W. 1974. Core and equilibria of a large economy. Princeton: Princeton University Press.Google Scholar
  4. Kantorovich, L.V., and G.P. Akilov. 1984. Functional analysis. London: Pergamon Press.Google Scholar
  5. Kantorovich, L.V., V.I. Zhiyanov, and A.G. Khovansky. 1978. The principle of differential optimization as applied to a singleproduct dynamical economic model. Sibirski matematicheskii zhurnal 19: 1053–1064.Google Scholar
  6. Kutateladze, S.S. 1983. Foundations of functional analysis. Novosibirsk: Nauka.Google Scholar
  7. Mas-Colell, A. 1975. A model of equilibrium with differentiated commodities. Journal of Mathematical Economics 2: 263–295.CrossRefGoogle Scholar
  8. Schaefer, H.H. 1971. Topological vector spaces. New York: Springer.CrossRefGoogle Scholar
  9. Smale, S. 1981. Global analysis and economics. In Handbook of mathematical economics, ed. K.J. Arrow and M.D. Intriligator, vol. 1. Amsterdam: North-Holland.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Leonid Kantorovich
    • 1
  • Victor Polterovich
    • 1
  1. 1.