Type of Publication: | Journal article |
Publication status: | Published |
URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-2-15q9c6q8vthbb5 |
Author: | Kaiser, Tobias; Speissegger, Patrick |
Year of publication: | 2019 |
Published in: | Transactions of the American Mathematical Society (TRAN) ; 371 (2019), 7. - pp. 5203-5246. - ISSN 0002-9947. - eISSN 1088-6850 |
ArXiv-ID: | arXiv:1708.04496v2 |
DOI (citable link): | https://dx.doi.org/10.1090/tran/7748 |
Summary: |
We describe maximal, in a sense made precise, L-analytic continuations of germs at +∞ of unary functions definable in the o-minimal structure Ran,exp on the Riemann surface L of the logarithm. As one application, we give an upper bound on the logarithmic-exponential complexity of the compositional inverse of an infinitely increasing such germ, in terms of its own logarithmic-exponential complexity and its level. As a second application, we strengthen Wilkie’s theorem on definable complex analytic continuations of germs belonging to the residue field Rpoly of the valuation ring of all polynomially bounded definable germs.
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Subject (DDC): | 510 Mathematics |
Link to License: | In Copyright |
Refereed: | Yes |
KAISER, Tobias, Patrick SPEISSEGGER, 2019. Analytic continuations of log-exp-analytic germs. In: Transactions of the American Mathematical Society (TRAN). 371(7), pp. 5203-5246. ISSN 0002-9947. eISSN 1088-6850. Available under: doi: 10.1090/tran/7748
@article{Kaiser2019Analy-40967.2, title={Analytic continuations of log-exp-analytic germs}, year={2019}, doi={10.1090/tran/7748}, number={7}, volume={371}, issn={0002-9947}, journal={Transactions of the American Mathematical Society (TRAN)}, pages={5203--5246}, author={Kaiser, Tobias and Speissegger, Patrick} }
Kaiser_2-15q9c6q8vthbb5.pdf | 266 |