2nd March 2010, 1500 MC206

from

NTU Singapore

will speak on

Representation of Functions in A^{−∞} by Dirichlet Series and Applications

Consider a space A^{−∞}(Ω) of holomorphic functions in a bounded convex domain Ω of **C**^{n}, with the so-called polynomial growth near the boundary ∂Ω. Introducing a space A^{∞}_{Ω} of entire functions with certain growth condition, we establish the mutual duality of A^{−∞}(Ω) and A^{−∞}. As one of applications of the obtained duality, a possibility of Ω representation of functions from both spaces A^{−∞}(Ω) and A^{−∞}_{Ω} in a form of Dirichlet series is given. These results are due to Abanin A.V. and myself.