Classes of Entire Analytic Functions of Unbounded Type on Banach Spaces
Keyword(s):
In this paper we investigate analytic functions of unbounded type on a complex infinite dimensional Banach space X. The main question is: under which conditions is there an analytic function of unbounded type on X such that its Taylor polynomials are in prescribed subspaces of polynomials? We obtain some sufficient conditions for a function f to be of unbounded type and show that there are various subalgebras of polynomials that support analytic functions of unbounded type. In particular, some examples of symmetric analytic functions of unbounded type are constructed.
2005 ◽
Vol 72
(2)
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pp. 299-315
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2005 ◽
Vol 57
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pp. 673-707
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2001 ◽
Vol 33
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pp. 443-453
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1988 ◽
Vol 103
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pp. 497-502
2011 ◽
Vol 53
(3)
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pp. 443-449
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