Let be a domain and let denote the Euclidean volume measure on .
is called the Bergman space on . The norm on this space is defined as
Further we define an inner product on as
The inner product as defined above really is an inner product and further it can be shown that is complete since convergence in the above norm implies normal convergence (uniform convergence on compact subsets). The space is therefore a Hilbert space. Sometimes this space is also denoted by .
- 1 D’Angelo, John P. , CRC Press, 1993.
- 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
|Date of creation||2013-03-22 15:04:43|
|Last modified on||2013-03-22 15:04:43|
|Last modified by||jirka (4157)|