{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:42:16Z","timestamp":1760150536239,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,5]],"date-time":"2023-12-05T00:00:00Z","timestamp":1701734400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Project of the Higher Education Institutions of the Autonomous Region","award":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"],"award-info":[{"award-number":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"]}]},{"name":"Doctoral Project of Hohhot Minzu College","award":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"],"award-info":[{"award-number":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"]}]},{"name":"Natural Science Foundation of China","award":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"],"award-info":[{"award-number":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"]}]},{"name":"Natural Science Foundation Inner Mongolia of China","award":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"],"award-info":[{"award-number":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"]}]},{"name":"Youth Innovative Talents Training Program of Inner Mongolia","award":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"],"award-info":[{"award-number":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"]}]},{"name":"National Universities\u2019 Huang-Danian Style Teacher Team","award":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"],"award-info":[{"award-number":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"]}]},{"name":"Inner Mongolia \u201cGrassland Talent Engineering\u201d Industrial Innovation Talent Team","award":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"],"award-info":[{"award-number":["NJZZ23097","MZXYBS202307","11761029","11761055","11661034","1196102","2017MS0123","Q2015031"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The symmetry of the spectrum and the completeness of the eigenfunction system of the Hamiltonian operator matrix have important applications in the symplectic Fourier expansion method in elasticity. However, the symplectic self-adjointness of Hamiltonian operator matrices is important to the characterization of the symmetry of the point spectrum. Therefore, in this paper, the symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied by using the spectral method of unbounded block operator matrices, and some sufficient conditions of the symplectic self-adjointness of infinite dimensional Hamiltonian operators are obtained. In addition, the necessary and sufficient conditions are also investigated for some special infinite dimensional Hamiltonian operators.<\/jats:p>","DOI":"10.3390\/sym15122163","type":"journal-article","created":{"date-parts":[[2023,12,5]],"date-time":"2023-12-05T08:09:17Z","timestamp":1701763757000},"page":"2163","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Symplectic Self-Adjointness of Hamiltonian Operator Matrices"],"prefix":"10.3390","volume":"15","author":[{"given":"Xiaohong","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Hohhot Minzu College, Hohhot 010051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junjie","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eerdun","family":"Buhe","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Hohhot Minzu College, Hohhot 010051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,5]]},"reference":[{"key":"ref_1","first-page":"173","article-title":"Completeness in the sense of Cauchy principal value of the eigenfunction systems of infinite dimensional Hamiltonian operator","volume":"5","author":"Chen","year":"2009","journal-title":"Sci. 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