Energy integrals and asymmetric co-potentials for closed forms

[2607.00853] Energy integrals and asymmetric co-potentials for closed forms Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Probability arXiv:2607.00853 (math) [Submitted on 1 Jul 2026 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Energy integrals and asymmetric co-potentials for closed forms Authors: Kazuhiro Kuwae , Takumu Ooi , Kaneharu Tsuchida , Toshihiro Uemura View a PDF of the paper titled Energy integrals and asymmetric co-potentials for closed forms, by Kazuhiro Kuwae and 3 other authors View PDF HTML (experimental) Abstract: We investigate the class of measures of finite energy integrals and the behavior of potentials and co-potentials associated with non-symmetric closed forms. In particular, we compare these objects with their symmetric counterparts from three viewpoints: a non-symmetric version of Stollmann--Voigt's inequality, non-symmetric perturbations of symmetric forms, and closed forms associated with non-symmetric jump-type forms. Our results indicate that measures of finite energy integrals, potentials, and co-potentials behave differently in the non-symmetric setting, requiring more delicate analysis than in the symmetric case. Comments: 30 pages Subjects: Probability (math.PR) ; Functional Analysis (math.FA) MSC classes: Primary 31C25, Secondary 60J46, 60J45, 47D08 Cite as: arXiv:2607.00853 [math.PR] (or arXiv:2607.00853v2 [math.PR] for this version) https://doi.org/10.48550/arXiv.2607.00853 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Takumu Ooi [ view email ] [v1] Wed, 1 Jul 2026 12:18:37 UTC (29 KB) [v2] Sat, 15 Aug 2026 05:23:21 UTC (29 KB) Full-text links: Access Paper: View a PDF of the paper titled Energy integrals and asymmetric co-potentials for closed forms, by Kazuhiro Kuwae and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.PR < prev | next > new | recent | 2026-07 Change to browse by: math math.FA References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Energy integrals and asymmetric co-potentials for closed forms#608920
• VARIATIONAL CALCULATIONS IN QUANTUM FIELD THEORY. PROCEEDINGS, INTERNATIONAL WORKSHOP, WANGEROOGE, F.R. GERMANY, SEPTEMBER 1-4, 1987#499113
• Inverse Semiclassical Scattering at Fixed Energy#822570
• A quasilinear elliptic equation with absorption term and Hardy potential *#208796
• Integrals of Products of Bessel Functions: An Insight from the Physics of Bloch Electrons#819210