Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators

Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators Acta Mathematica Sinica, English Series Acta Mathematica Sinica, Published online: May 30, 2018 https://doi.org/10.1007/s10114-018-7267-7 English Series http://www.ActaMath.com Springer-Verlag GmbH Germany & The Editorial Office of AMS 2018 Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators Lin LI School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China Department of Physiology, Hetao College, Bayannur 015000, P.R.China E-mail : lilinneida@126.com 1) Alatancang CHEN Department of Mathematics, Hohhot Minzu College, Hohhot 010051, P.R.China E-mail : alatanca@imu.edu.cn De Yu WU School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China E-mail : deyuwu@imu.edu.cn Abstract Symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied, the necessary and sufficient conditions are given. Using the relatively bounded perturbation, the sufficient conditions about symplectic self-adjointness are shown. Keywords Hamiltonian operator, symplectic self-adjointness, quadratic complement, relative bound MR(2010) Subject Classification 47A05, 47B25, 47E05 1 Introduction In physics and mechanics, many classical problems are expressed as partial differential equations (PDEs), such as the famous Schro ¨dinger equations, the KdV equations, the Maxwell equations and the Riccati equation and so on [8, 9, 12, 13, 23]. Most of them can be equivalently written −1 δH 0 I δ as Hamiltonian canonical equations u ˙ = J , where J = ,and http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Sinica, English Series Springer Journals

Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators

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Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Copyright
Copyright © 2018 by Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1439-8516
eISSN
1439-7617
D.O.I.
10.1007/s10114-018-7267-7
Publisher site
See Article on Publisher Site

Abstract

Acta Mathematica Sinica, English Series Acta Mathematica Sinica, Published online: May 30, 2018 https://doi.org/10.1007/s10114-018-7267-7 English Series http://www.ActaMath.com Springer-Verlag GmbH Germany & The Editorial Office of AMS 2018 Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators Lin LI School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China Department of Physiology, Hetao College, Bayannur 015000, P.R.China E-mail : lilinneida@126.com 1) Alatancang CHEN Department of Mathematics, Hohhot Minzu College, Hohhot 010051, P.R.China E-mail : alatanca@imu.edu.cn De Yu WU School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China E-mail : deyuwu@imu.edu.cn Abstract Symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied, the necessary and sufficient conditions are given. Using the relatively bounded perturbation, the sufficient conditions about symplectic self-adjointness are shown. Keywords Hamiltonian operator, symplectic self-adjointness, quadratic complement, relative bound MR(2010) Subject Classification 47A05, 47B25, 47E05 1 Introduction In physics and mechanics, many classical problems are expressed as partial differential equations (PDEs), such as the famous Schro ¨dinger equations, the KdV equations, the Maxwell equations and the Riccati equation and so on [8, 9, 12, 13, 23]. Most of them can be equivalently written −1 δH 0 I δ as Hamiltonian canonical equations u ˙ = J , where J = ,and

Journal

Acta Mathematica Sinica, English SeriesSpringer Journals

Published: May 31, 2018

References

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