{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:12:30Z","timestamp":1750219950327,"version":"3.41.0"},"reference-count":4,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T00:00:00Z","timestamp":1677628800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2023,3]]},"abstract":"<jats:p>\n            The notion of lacunary infinite numerical sequence is introduced. It is shown that for an arbitrary linear difference operator\n            <jats:italic>L<\/jats:italic>\n            with coefficients belonging to the set\n            <jats:italic>R<\/jats:italic>\n            of infinite numerical sequences, a criterion (i.e., a necessary and sufficient condition) for the infinite-dimensionality of its space\n            <jats:italic>\n              V\n              <jats:sub>L<\/jats:sub>\n            <\/jats:italic>\n            of solutions belonging to\n            <jats:italic>R<\/jats:italic>\n            is the presence of a lacunary sequence in\n            <jats:italic>\n              V\n              <jats:sub>L<\/jats:sub>\n              .\n            <\/jats:italic>\n          <\/jats:p>","DOI":"10.1145\/3610377.3610378","type":"journal-article","created":{"date-parts":[[2023,7,19]],"date-time":"2023-07-19T20:23:33Z","timestamp":1689798213000},"page":"1-4","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Linear Difference Operators with Sequence Coefficients Having Infinite-Dimentional Solution Spaces"],"prefix":"10.1145","volume":"57","author":[{"given":"Sergei","family":"Abramov","sequence":"first","affiliation":[{"name":"Federal Research Center \"Computer Science and Control,\" Russian Academy of Sciences, Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gleb","family":"Pogudin","sequence":"additional","affiliation":[{"name":"LIX, CNRS, \u00c9cole polytechnique, Institute Polytechnique de Paris, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2023,7,19]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1134\/S0965542521100018"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.4171\/JEMS\/968"},{"key":"e_1_2_1_3_1","first-page":"e33","article-title":"Solving difference equations in sequences: Universality and Undecidability. Forum of Mathematics","volume":"8","author":"Pogudin G.","year":"2020","unstructured":"G. Pogudin , T. Scanlon , M. Wibmer . Solving difference equations in sequences: Universality and Undecidability. Forum of Mathematics , Sigma , 2020 , Vol. 8 , e33 . G. Pogudin, T. Scanlon, M. Wibmer. Solving difference equations in sequences: Universality and Undecidability. Forum of Mathematics, Sigma, 2020, Vol. 8, e33.","journal-title":"Sigma"},{"key":"e_1_2_1_4_1","volume-title":"Advances in Applied Mathematics","volume":"123","author":"Wibmer M.","year":"2021","unstructured":"M. Wibmer , On the dimension of systems of algebraic difference equations . Advances in Applied Mathematics , 2021 , Vol. 123 . M. Wibmer, On the dimension of systems of algebraic difference equations. Advances in Applied Mathematics, 2021, Vol. 123."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3610377.3610378","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3610377.3610378","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T17:49:02Z","timestamp":1750182542000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3610377.3610378"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["10.1145\/3610377.3610378"],"URL":"https:\/\/doi.org\/10.1145\/3610377.3610378","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2023,3]]},"assertion":[{"value":"2023-07-19","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}