{"date_updated":"2022-03-02T14:44:34Z","publisher":"Springer Nature","department":[{"_id":"JaMa"}],"abstract":[{"lang":"eng","text":"We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique."}],"citation":{"mla":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” <i>Potential Analysis</i>, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s11118-021-09951-y\">10.1007/s11118-021-09951-y</a>.","ama":"Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals and applications. <i>Potential Analysis</i>. 2021. doi:<a href=\"https://doi.org/10.1007/s11118-021-09951-y\">10.1007/s11118-021-09951-y</a>","chicago":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” <i>Potential Analysis</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s11118-021-09951-y\">https://doi.org/10.1007/s11118-021-09951-y</a>.","short":"L. Dello Schiavo, Potential Analysis (2021).","ieee":"L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals and applications,” <i>Potential Analysis</i>. Springer Nature, 2021.","ista":"Dello Schiavo L. 2021. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis.","apa":"Dello Schiavo, L. (2021). Ergodic decomposition of Dirichlet forms via direct integrals and applications. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-021-09951-y\">https://doi.org/10.1007/s11118-021-09951-y</a>"},"license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"author":[{"last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","first_name":"Lorenzo"}],"type":"journal_article","language":[{"iso":"eng"}],"title":"Ergodic decomposition of Dirichlet forms via direct integrals and applications","status":"public","external_id":{"arxiv":["2003.01366"]},"doi":"10.1007/s11118-021-09951-y","main_file_link":[{"open_access":"1","url":"https://dx.doi.org/10.1007/s11118-021-09951-y"}],"_id":"10145","article_processing_charge":"Yes (via OA deal)","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020"}],"scopus_import":"1","month":"10","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa_version":"Published Version","date_published":"2021-10-06T00:00:00Z","publication_identifier":{"eissn":["1572-929X"],"issn":["0926-2601"]},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa":1,"date_created":"2021-10-17T22:01:17Z","day":"06","publication_status":"epub_ahead","quality_controlled":"1","publication":"Potential Analysis","article_type":"original","acknowledgement":"The author is grateful to Professors Sergio Albeverio and Andreas Eberle, and to Dr. Kohei Suzuki, for fruitful conversations on the subject of the present work, and for respectively pointing out the references [1, 13], and [3, 20]. Finally, he is especially grateful to an anonymous Reviewer for their very careful reading and their suggestions which improved the readability of the paper.","year":"2021"}