American Mathematical Society

Book Review

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MathSciNet review: 3686324
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Book Information:

Authors: Leonid Polterovich and Daniel Rosen
Title: Function theory on symplectic manifolds
Additional book information: CRM Monograph series, vol. 34, American Mathematical Society, Providence, Rhode Island, 2014, xii+203 pp., ISBN 978-1-4704-1693-5

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Lev Buhovsky, The $2/3$-convergence rate for the Poisson bracket, Geom. Funct. Anal. 19 (2010), no. 6, 1620–1649. MR 2594616, DOI 10.1007/s00039-010-0045-z

Lev Buhovsky and Yaron Ostrover, On the uniqueness of Hofer’s geometry, Geom. Funct. Anal. 21 (2011), no. 6, 1296–1330. MR 2860189, DOI 10.1007/s00039-011-0143-6

Lev Buhovsky, Michael Entov, and Leonid Polterovich, Poisson brackets and symplectic invariants, Selecta Math. (N.S.) 18 (2012), no. 1, 89–157. MR 2891862, DOI 10.1007/s00029-011-0068-9

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Y. Eliashberg, Rigidity of symplectic structures, preprint, 1981.

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Michael Entov and Leonid Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not. 30 (2003), 1635–1676. MR 1979584, DOI 10.1155/S1073792803210011

Michael Entov and Leonid Polterovich, $C^0$-rigidity of Poisson brackets, Symplectic topology and measure preserving dynamical systems, Contemp. Math., vol. 512, Amer. Math. Soc., Providence, RI, 2010, pp. 25–32. MR 2605312, DOI 10.1090/conm/512/10058

Michael Entov and Leonid Polterovich, Quasi-states and symplectic intersections, Comment. Math. Helv. 81 (2006), no. 1, 75–99. MR 2208798, DOI 10.4171/CMH/43

Andrew M. Gleason, Measures on the closed subspaces of a Hilbert space, J. Math. Mech. 6 (1957), 885–893. MR 0096113, DOI 10.1512/iumj.1957.6.56050

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H. Hofer, On the topological properties of symplectic maps, Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), no. 1-2, 25–38. MR 1059642, DOI 10.1017/S0308210500024549

Leonid Polterovich, Quantum unsharpness and symplectic rigidity, Lett. Math. Phys. 102 (2012), no. 3, 245–264. MR 2989482, DOI 10.1007/s11005-012-0564-7

Leonid Polterovich, Symplectic geometry of quantum noise, Comm. Math. Phys. 327 (2014), no. 2, 481–519. MR 3183407, DOI 10.1007/s00220-014-1937-9

Frol Zapolsky, Quasi-states and the Poisson bracket on surfaces, J. Mod. Dyn. 1 (2007), no. 3, 465–475. MR 2318499, DOI 10.3934/jmd.2007.1.465

Review Information:

Reviewer: Yakov Eliashberg
Affiliation: Department of Mathematics, Stanford University
Email: eliash@stanford.edu