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Sharpness of Zapolsky's inequality for quasi-states and Poisson brackets
1. | School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel |
References:
[1] |
J. F. Aarnes, Quasi-states and quasi-measures, Adv. Math., 86 (1991), 41-67.
doi: 10.1016/0001-8708(91)90035-6. |
[2] |
J. F. Aarnes, Pure quasi-states and extremal quasi-measures, Math. Ann., 295 (1993), 575-588.
doi: 10.1007/BF01444904. |
[3] |
J. F. Aarnes, Construction of non-sub-additive measures and discretization of Borel measures, Fund. Math., 147 (1995), 213-237. |
[4] |
A. Amir, Sharpness of Zapolsky inequality for quasi-states and Poisson brackets, preprint, arXiv:1101.1599. |
[5] |
L. Buhovsky, M. Entov and L. Polterovich, Poisson brackets and symplectic invariants, preprint, arXiv:1103.3198. |
[6] |
M. Entov and L. Polterovich, Quasi-states and symplectic intersections, Comment. Math. Helv., 81 (2006), 75-99.
doi: 10.4171/CMH/43. |
[7] |
M. Entov, L. Polterovich and F. Zapolsky, An "anti-Gleason" phenomenon and simultaneous measurements in classical mechanics, Foundations of Physics, 37 (2007), 1306-1316.
doi: 10.1007/s10701-007-9158-0. |
[8] |
M. Entov, L. Polterovich and F. Zapolsky, Quasi-morphisms and the Poisson bracket, Pure Appl. Math. Q., 3 (2007), part 1, 1037-1055. |
[9] |
V. Guillemin and A. Pollack, "Differential Topology," Prentice-Hall, Inc., Englewood Cliffs, NJ, 1974. |
[10] |
F. F. Knudsen, Topology and the construction of extreme quasi-measures, Adv. Math., 120 (1996), 302-321.
doi: 10.1006/aima.1996.0041. |
[11] |
F. F. Knudsen, New topological measures on the torus, Fund. Math., 185 (2005), 287-293.
doi: 10.4064/fm185-3-6. |
[12] |
S. Lang, "Differential and Riemannian Manifolds," 3rd ed., Graduate Texts in Mathematics, 160, Springer-Verlag, New York, 1995. |
[13] |
M. E. Taylor, "Measure Theory and Integration," Graduate Studies in Mathematics, 76, American Mathematical Society, Providence, RI, 2006. |
[14] |
F. Zapolsky, Isotopy-invariant topological measures on closed orientable surfaces of higher genus, Math. Zeit., available from: http://www.springerlink.com/content/94765t4230021783/.
doi: 10.1007/s00209-0100788-0. |
[15] |
F. Zapolsky, Quasi-states and the Poisson bracket on surfaces, J. Mod. Dyn., 1 (2007), 465-475. |
[16] |
F. Zapolsky, "Quasi-States and Symplectic Topology," Ph.D. thesis, Tel-Aviv University, 2009. |
show all references
References:
[1] |
J. F. Aarnes, Quasi-states and quasi-measures, Adv. Math., 86 (1991), 41-67.
doi: 10.1016/0001-8708(91)90035-6. |
[2] |
J. F. Aarnes, Pure quasi-states and extremal quasi-measures, Math. Ann., 295 (1993), 575-588.
doi: 10.1007/BF01444904. |
[3] |
J. F. Aarnes, Construction of non-sub-additive measures and discretization of Borel measures, Fund. Math., 147 (1995), 213-237. |
[4] |
A. Amir, Sharpness of Zapolsky inequality for quasi-states and Poisson brackets, preprint, arXiv:1101.1599. |
[5] |
L. Buhovsky, M. Entov and L. Polterovich, Poisson brackets and symplectic invariants, preprint, arXiv:1103.3198. |
[6] |
M. Entov and L. Polterovich, Quasi-states and symplectic intersections, Comment. Math. Helv., 81 (2006), 75-99.
doi: 10.4171/CMH/43. |
[7] |
M. Entov, L. Polterovich and F. Zapolsky, An "anti-Gleason" phenomenon and simultaneous measurements in classical mechanics, Foundations of Physics, 37 (2007), 1306-1316.
doi: 10.1007/s10701-007-9158-0. |
[8] |
M. Entov, L. Polterovich and F. Zapolsky, Quasi-morphisms and the Poisson bracket, Pure Appl. Math. Q., 3 (2007), part 1, 1037-1055. |
[9] |
V. Guillemin and A. Pollack, "Differential Topology," Prentice-Hall, Inc., Englewood Cliffs, NJ, 1974. |
[10] |
F. F. Knudsen, Topology and the construction of extreme quasi-measures, Adv. Math., 120 (1996), 302-321.
doi: 10.1006/aima.1996.0041. |
[11] |
F. F. Knudsen, New topological measures on the torus, Fund. Math., 185 (2005), 287-293.
doi: 10.4064/fm185-3-6. |
[12] |
S. Lang, "Differential and Riemannian Manifolds," 3rd ed., Graduate Texts in Mathematics, 160, Springer-Verlag, New York, 1995. |
[13] |
M. E. Taylor, "Measure Theory and Integration," Graduate Studies in Mathematics, 76, American Mathematical Society, Providence, RI, 2006. |
[14] |
F. Zapolsky, Isotopy-invariant topological measures on closed orientable surfaces of higher genus, Math. Zeit., available from: http://www.springerlink.com/content/94765t4230021783/.
doi: 10.1007/s00209-0100788-0. |
[15] |
F. Zapolsky, Quasi-states and the Poisson bracket on surfaces, J. Mod. Dyn., 1 (2007), 465-475. |
[16] |
F. Zapolsky, "Quasi-States and Symplectic Topology," Ph.D. thesis, Tel-Aviv University, 2009. |
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