Summary: Hardy and Hilbert
N.A.
2007
Notation: D = {z C : |z| < 1} is the unit disc in C. Its boundary is
the unit circle S = {z C : |z| = 1}. H(D) is the space of the holomorpihc
functions on D; h(D) is the space of the harmonic functions on D. The spaces
2
(N), 2
(Z) are the 2
-spaces of C-valued sequences with indices in N, Z, re-
spectively:
a = {an}, b = {bn} : a, b 2 =
n
anbn.
The basic structure is induced by the inclusion N Z:
2
(Z) = 2
(N) 2
(Z - N); 2
(Z - N)

Source: Arcozzi, Nicola - Dipartimento di Matematica, Università di Bologna

Collections: Mathematics