Let be an open subset of the complex plane , and let denote the collection of all analytic functions whose complex modulus is square integrable with respect to area measure. Then , sometimes also denoted , is called the Bergman space for . Thus, the Bergman space consists of all the analytic functions in . The Bergman space can also be generalized to , where .
Bergman Space
See also
Hardy SpaceExplore with Wolfram|Alpha
References
Hedenmalm, H.; Korenblum, B.; and Zhu, K. Theory of Bergman Spaces. New York: Springer-Verlag, 2000.Shields, A. L. "Weighted Shift Operators and Analytic Function Theory." In Topics in Operator Theory (Ed. C. Pearcy). Providence, RI: Amer. Math. Soc., pp. 49-128, 1979.Zhu, K. Operator Theory in Function Spaces. New York: Dekker, 1990.Referenced on Wolfram|Alpha
Bergman SpaceCite this as:
Weisstein, Eric W. "Bergman Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BergmanSpace.html