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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Uniform estimate for a segment function in terms of a polynomial strip


Authors: S. I. Dudov and E. V. Sorina
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 24 (2012), nomer 5.
Journal: St. Petersburg Math. J. 24 (2013), 723-742
MSC (2010): Primary 90C05
Published electronically: July 24, 2013
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Abstract: A problem about a uniform estimate for a continuous segment function in terms of a polynomial strip is considered. The problem reduces to a convex programming problem the target function of which is equal to the sum of the target functions for the inner and outer estimate of the same segment function via a polynomial strip. Convex analysis tools are used to obtain necessary and sufficient conditions for being a solution, and also uniqueness conditions in a form resembling the Chebyshov alternance.


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Additional Information

S. I. Dudov
Affiliation: Saratov state university, Astrakhanskaya str. 83, Saratov 410012, Russia
Email: DudovSI@info.sgu.ru

E. V. Sorina
Affiliation: Saratov state university, Astrakhanskaya str. 83, Saratov 410012, Russia
Email: sorina@rol.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2013-01262-3
PII: S 1061-0022(2013)01262-3
Keywords: Segment function, polynomial strip, uniform estimate, subdifferential, alternance
Received by editor(s): September 9, 2011
Published electronically: July 24, 2013
Additional Notes: The author was supported by RFBR (grant no. 10-01-00270-a) and by the NSh grant NSh-4383.2010.1.
Article copyright: © Copyright 2013 American Mathematical Society