On the representation of analytic functions by infinite series
1953 ◽
Vol 245
(900)
◽
pp. 429-468
◽
Keyword(s):
Given a set of functions {p k {z)}, necessary and sufficient conditions are known under which the basic series ∑ (k=0) ∞ II k f (0)p k (z) will represent all functions f ( z ) in certain classes. The various cases are included in a general theory given in part II. Questions of uniqueness are discussed, and an attempt is made to initiate a theory of representation by series of the form ∑ (k=0) ∞ α k p k (z) which are not necessarily basic. Topological methods are used, and part I is devoted largely to preliminaries. In part III is discussed the relationship between given sets and various associated sets such as the inverse and product sets.
2006 ◽
Vol 4
(1)
◽
pp. 73-84
◽
2020 ◽
Vol 24
(2)
◽
pp. 241-251
2020 ◽
Vol ahead-of-print
(ahead-of-print)
◽
1983 ◽
Vol 15
(04)
◽
pp. 752-768
◽
2019 ◽
Vol 13
(2)
◽
pp. 104-111
1975 ◽
Vol 18
(1)
◽
pp. 7-17
◽