{"abstract":[{"lang":"eng","text":"In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established."}],"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.1804.08353"}],"department":[{"_id":"JaMa"}],"issue":"8","publication_status":"published","date_published":"2023-08-01T00:00:00Z","date_updated":"2023-11-14T13:07:09Z","article_processing_charge":"No","month":"08","day":"01","type":"journal_article","status":"public","quality_controlled":"1","title":"Sobolev-type inequalities and eigenvalue growth on graphs with finite measure","scopus_import":"1","publisher":"American Mathematical Society","date_created":"2023-07-02T22:00:43Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"oa_version":"Preprint","language":[{"iso":"eng"}],"_id":"13177","article_type":"original","citation":{"short":"B. Hua, M. Keller, M. Schwarz, M. Wirth, Proceedings of the American Mathematical Society 151 (2023) 3401–3414.","ama":"Hua B, Keller M, Schwarz M, Wirth M. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. <i>Proceedings of the American Mathematical Society</i>. 2023;151(8):3401-3414. doi:<a href=\"https://doi.org/10.1090/proc/14361\">10.1090/proc/14361</a>","chicago":"Hua, Bobo, Matthias Keller, Michael Schwarz, and Melchior Wirth. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2023. <a href=\"https://doi.org/10.1090/proc/14361\">https://doi.org/10.1090/proc/14361</a>.","ista":"Hua B, Keller M, Schwarz M, Wirth M. 2023. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. 151(8), 3401–3414.","apa":"Hua, B., Keller, M., Schwarz, M., &#38; Wirth, M. (2023). Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/14361\">https://doi.org/10.1090/proc/14361</a>","ieee":"B. Hua, M. Keller, M. Schwarz, and M. Wirth, “Sobolev-type inequalities and eigenvalue growth on graphs with finite measure,” <i>Proceedings of the American Mathematical Society</i>, vol. 151, no. 8. American Mathematical Society, pp. 3401–3414, 2023.","mla":"Hua, Bobo, et al. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” <i>Proceedings of the American Mathematical Society</i>, vol. 151, no. 8, American Mathematical Society, 2023, pp. 3401–14, doi:<a href=\"https://doi.org/10.1090/proc/14361\">10.1090/proc/14361</a>."},"publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"external_id":{"arxiv":["1804.08353"],"isi":["000988204400001"]},"page":"3401-3414","doi":"10.1090/proc/14361","publication":"Proceedings of the American Mathematical Society","author":[{"first_name":"Bobo","last_name":"Hua","full_name":"Hua, Bobo"},{"last_name":"Keller","first_name":"Matthias","full_name":"Keller, Matthias"},{"full_name":"Schwarz, Michael","last_name":"Schwarz","first_name":"Michael"},{"full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","first_name":"Melchior","orcid":"0000-0002-0519-4241"}],"acknowledgement":"The second author was supported by the priority program SPP2026 of the German Research Foundation (DFG). The fourth author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2.","isi":1,"year":"2023","volume":151,"intvolume":"       151"}