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Chebyshev measures
Author(s):
Raphaël
Cerf;
Carlo
Mariconda
Journal:
Proc. Amer. Math. Soc.
125
(1997),
3321-3329.
MSC (1991):
Primary 41A50, 46G10, 52A20
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Abstract:
We introduce Chebyshev measures. We generalize the representation theorem concerning both measures admitting a density function which is a  -system and oriented measures.
References:
- 1.
- R. Cerf - C. Mariconda, On bang-bang constrained solutions of a control system, SIAM J. Control Optim. 33 (1995), 554-567. MR 95m:49019
- 2.
- R. Cerf - C. Mariconda, Oriented measures with continuous densities and the bang-bang principle, J. Funct. Anal. 126 (1994), 476-505. MR 95k:49015
- 3.
- R. Cerf - C. Mariconda, Oriented measures, J. Math. Anal. Appl. 197 (1996), 925-944. CMP 96:07
- 4.
- S. Karlin - W.J. Studden, Tchebycheff systems: with applications in analysis and statistics, Pure and applied mathematics, John Wiley & Sons, New York, 1966. MR 34:4757
- 5.
- M.G. Krein - A.A. Nudel'man, The Markov moment problems and extremal problems, Transl. Math. Monographs, vol. 50, AMS, Providence, Rhode Island, 1977. MR 56:16284
- 6.
- N.G. Lloyd, Degree theory, Cambridge University Press, Cambridge, 1978. MR 58:12558
- 7.
- R.T. Rockafeller, Convex Analysis, Princeton University Press, Princeton, New Jersey, 1972.
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Additional Information:
Raphaël
Cerf
Affiliation:
Université Paris sud, Mathématiques, bâtiment 425, 91405 Orsay Cedex, France
Email:
Raphael.Cerf@math.u-psud.fr
Carlo
Mariconda
Affiliation:
Dipartimento di Matematica pura e applicata, Università di Padova, 7 via Belzoni, 35131 Padova, Italy
Email:
mariconda@math.unipd.it
DOI:
10.1090/S0002-9939-97-04095-1
PII:
S 0002-9939(97)04095-1
Keywords:
Oriented measure,
vector measure,
Lyapunov,
Chebyshev,
$T$--system
Received by editor(s):
August 29, 1995
Received by editor(s) in revised form:
June 13, 1996
Additional Notes:
The second author (C.M.) was supported by a Grant of the Consiglio Nazionale delle Ricerche (Grant 203.01.62).
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1997,
American Mathematical Society
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