Lower Bounds on the Continuation of Holomorphic Functions | Zendy

Robert Rettinger | Zendy

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Lower Bounds on the Continuation of Holomorphic Functions

Author(s) -

Robert Rettinger

Publication year - 2008

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2008.12.018

Subject(s) - continuation , holomorphic function , mathematics , domain (mathematical analysis) , combinatorics , discrete mathematics , pure mathematics , computer science , mathematical analysis , programming language

We show that continuation of holomorphic functions needs time at least Ω(n2) in the uniform case, which is optimal up to a polylogarithmic factor. In the non-uniform case, i.e. assuming f to be computable in time O(t) on an open subset of its domain, we show, that continuation of f cannot be robustly done in time o(n⋅t(n)). This again is optimal up to a polylogarithmic factor

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