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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.
doi: 10.1016/0001-8708(91)90035-6. |
[2] |
J. F. Aarnes, Pure quasi-states and extremal quasi-measures,, Math. Ann., 295 (1993), 575.
doi: 10.1007/BF01444904. |
[3] |
J. F. Aarnes, Construction of non-sub-additive measures and discretization of Borel measures,, Fund. Math., 147 (1995), 213.
|
[4] |
A. Amir, Sharpness of Zapolsky inequality for quasi-states and Poisson brackets,, preprint, (). Google Scholar |
[5] |
L. Buhovsky, M. Entov and L. Polterovich, Poisson brackets and symplectic invariants,, preprint, (). Google Scholar |
[6] |
M. Entov and L. Polterovich, Quasi-states and symplectic intersections,, Comment. Math. Helv., 81 (2006), 75.
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.
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), 1037.
|
[9] |
V. Guillemin and A. Pollack, "Differential Topology,", Prentice-Hall, (1974).
|
[10] |
F. F. Knudsen, Topology and the construction of extreme quasi-measures,, Adv. Math., 120 (1996), 302.
doi: 10.1006/aima.1996.0041. |
[11] |
F. F. Knudsen, New topological measures on the torus,, Fund. Math., 185 (2005), 287.
doi: 10.4064/fm185-3-6. |
[12] |
S. Lang, "Differential and Riemannian Manifolds,", 3rd ed., 160 (1995).
|
[13] |
M. E. Taylor, "Measure Theory and Integration,", Graduate Studies in Mathematics, 76 (2006).
|
[14] |
F. Zapolsky, Isotopy-invariant topological measures on closed orientable surfaces of higher genus,, Math. Zeit., ().
doi: 10.1007/s00209-0100788-0. |
[15] |
F. Zapolsky, Quasi-states and the Poisson bracket on surfaces,, J. Mod. Dyn., 1 (2007), 465.
|
[16] |
F. Zapolsky, "Quasi-States and Symplectic Topology,", Ph.D. thesis, (2009). Google Scholar |
show all references
References:
[1] |
J. F. Aarnes, Quasi-states and quasi-measures,, Adv. Math., 86 (1991), 41.
doi: 10.1016/0001-8708(91)90035-6. |
[2] |
J. F. Aarnes, Pure quasi-states and extremal quasi-measures,, Math. Ann., 295 (1993), 575.
doi: 10.1007/BF01444904. |
[3] |
J. F. Aarnes, Construction of non-sub-additive measures and discretization of Borel measures,, Fund. Math., 147 (1995), 213.
|
[4] |
A. Amir, Sharpness of Zapolsky inequality for quasi-states and Poisson brackets,, preprint, (). Google Scholar |
[5] |
L. Buhovsky, M. Entov and L. Polterovich, Poisson brackets and symplectic invariants,, preprint, (). Google Scholar |
[6] |
M. Entov and L. Polterovich, Quasi-states and symplectic intersections,, Comment. Math. Helv., 81 (2006), 75.
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.
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), 1037.
|
[9] |
V. Guillemin and A. Pollack, "Differential Topology,", Prentice-Hall, (1974).
|
[10] |
F. F. Knudsen, Topology and the construction of extreme quasi-measures,, Adv. Math., 120 (1996), 302.
doi: 10.1006/aima.1996.0041. |
[11] |
F. F. Knudsen, New topological measures on the torus,, Fund. Math., 185 (2005), 287.
doi: 10.4064/fm185-3-6. |
[12] |
S. Lang, "Differential and Riemannian Manifolds,", 3rd ed., 160 (1995).
|
[13] |
M. E. Taylor, "Measure Theory and Integration,", Graduate Studies in Mathematics, 76 (2006).
|
[14] |
F. Zapolsky, Isotopy-invariant topological measures on closed orientable surfaces of higher genus,, Math. Zeit., ().
doi: 10.1007/s00209-0100788-0. |
[15] |
F. Zapolsky, Quasi-states and the Poisson bracket on surfaces,, J. Mod. Dyn., 1 (2007), 465.
|
[16] |
F. Zapolsky, "Quasi-States and Symplectic Topology,", Ph.D. thesis, (2009). Google Scholar |
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