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# Functional Analysis

Functional analysis is a branch of mathematics concerned with infinite-dimensional vector spaces (mainly function spaces) and mappings between them. The spaces may be of different, and possibly infinite, dimensions. These mappings are called operators or, if the range is on the real line or in the complex plane, functionals.

## See also

Functional, Functional Equation, Generalized Function, Operator Explore this topic in the MathWorld classroom

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## References

Balakrishnan, A. V. Applied Functional Analysis, 2nd ed. New York: Springer-Verlag, 1981.Berezansky, Y. M.; Us, G. F.; and Sheftel, Z. G. Functional Analysis, Vol. 1. Boston, MA: Birkhäuser, 1996.Berezansky, Y. M.; Us, G. F.; and Sheftel, Z. G. Functional Analysis, Vol. 2. Boston, MA: Birkhäuser, 1996.Birkhoff, G. and Kreyszig, E. "The Establishment of Functional Analysis." Historia Math. 11, 258-321, 1984.Hutson, V. and Pym, J. S. Applications of Functional Analysis and Operator Theory. New York: Academic Press, 1980.Kreyszig, E. Introductory Functional Analysis with Applications. New York: Wiley, 1989.Reed, M. and Simon, B. Methods of Modern Mathematical Physics, Vol. 1: Functional Analysis. New York: Academic Press, 1972.Yoshida, K. Functional Analysis and Its Applications. New York: Springer-Verlag, 1971.Zeidler, E. Nonlinear Functional Analysis and Its Applications. New York: Springer-Verlag, 1989.Zeidler, E. Applied Functional Analysis: Applications to Mathematical Physics. New York: Springer-Verlag, 1995.

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Functional Analysis

## Cite this as:

Weisstein, Eric W. "Functional Analysis." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FunctionalAnalysis.html