Reconstruction of algebraic sets from dynamic moments

Gabriela Putinar[1]; Mihai Putinar[1]

  • [1] Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.

Annales de la faculté des sciences de Toulouse Mathématiques (2007)

  • Volume: 16, Issue: 3, page 647-664
  • ISSN: 0240-2963

Abstract

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We discuss an exact reconstruction algorithm for time expanding semi-algebraic sets given by a single polynomial inequality. The theoretical motivation comes from the classical L -problem of moments, while some possible applications to 2D fluid moving boundaries are sketched. The proofs rely on an adapted co-area theorem and a Hankel form minimization.

How to cite

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Putinar, Gabriela, and Putinar, Mihai. "Reconstruction of algebraic sets from dynamic moments." Annales de la faculté des sciences de Toulouse Mathématiques 16.3 (2007): 647-664. <http://eudml.org/doc/10066>.

@article{Putinar2007,
abstract = {We discuss an exact reconstruction algorithm for time expanding semi-algebraic sets given by a single polynomial inequality. The theoretical motivation comes from the classical $L$-problem of moments, while some possible applications to 2D fluid moving boundaries are sketched. The proofs rely on an adapted co-area theorem and a Hankel form minimization.},
affiliation = {Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.; Department of Mathematics, University of California, Santa Barbara, CA 93106, U.S.A.},
author = {Putinar, Gabriela, Putinar, Mihai},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
number = {3},
pages = {647-664},
publisher = {Université Paul Sabatier, Toulouse},
title = {Reconstruction of algebraic sets from dynamic moments},
url = {http://eudml.org/doc/10066},
volume = {16},
year = {2007},
}

TY - JOUR
AU - Putinar, Gabriela
AU - Putinar, Mihai
TI - Reconstruction of algebraic sets from dynamic moments
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2007
PB - Université Paul Sabatier, Toulouse
VL - 16
IS - 3
SP - 647
EP - 664
AB - We discuss an exact reconstruction algorithm for time expanding semi-algebraic sets given by a single polynomial inequality. The theoretical motivation comes from the classical $L$-problem of moments, while some possible applications to 2D fluid moving boundaries are sketched. The proofs rely on an adapted co-area theorem and a Hankel form minimization.
LA - eng
UR - http://eudml.org/doc/10066
ER -

References

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  8. Gustafsson (B.), He (C.), Milanfar (P.), Putinar (M.).— Reconstructing planar domains from their moments. Inverse Problems 16, no. 4, p. 1053-1070 (2000). Zbl0959.44010MR1776483
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  10. Gustafsson (B.), Vasiliev (A.).— Conformal and Potential Analysis in Hele-Shaw Cells, Birkhauser, Basel (2006). Zbl1122.76002MR2245542
  11. Karlin (S.), Studden (W. J.).— Tchebycheff systems: With applications in analysis and statistics. Pure and Applied Mathematics, Vol. XV Interscience Publishers John Wiley & Sons (1966). Zbl0153.38902MR204922
  12. Krein (M. G.), Nudelman (A. A.).— The Markov moment problem and extremal problems. Translations of Mathematical Monographs, Vol. 50. A. M. S., Providence, R.I. (1977). Zbl0361.42014
  13. Putinar (G.).— Asymptotics for extremal moments and monodromy of complex singularities. preprint UCSB, no. 2006-48. 
  14. Putinar (G.).— Semi-local micro-differential theory and computations of moments for semi-algebraic domains. preprint UCSB, no. 2006-46. 
  15. Putinar (M.).— Extremal solutions of the two-dimensional L -problem of moments. II. J. Approx. Theory 92, no. 1, p. 38-58 (1998). Zbl0910.47011MR1492857

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