{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:31:59Z","timestamp":1787232719502,"version":"build-2736575974"},"reference-count":7,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2007,1]]},"abstract":"<jats:p>We define a notion of determining sets for the discrete Laplacian in a domain \u03a9. A set D is called determining if harmonic functions are uniquely determined by providing their values on D, and if D has the same size as the boundary of \u03a9. It is shown that there exist determining sets that are fairly evenly distributed in \u03a9. A number of basic properties of determining sets are derived.<\/jats:p>","DOI":"10.1137\/050645233","type":"journal-article","created":{"date-parts":[[2007,4,30]],"date-time":"2007-04-30T18:00:35Z","timestamp":1177956035000},"page":"315-324","source":"Crossref","is-referenced-by-count":1,"title":["Determining Sets for the Discrete Laplacian"],"prefix":"10.1137","volume":"49","author":[{"given":"Aviad","family":"Rubinstein","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jacob","family":"Rubinstein","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gershon","family":"Wolansky","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,5,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1364\/OL.31.001845"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/j.optcom.2003.12.020"},{"key":"R3","unstructured":"D. Malacara,\n                      Optical Shop Testing\n                      , 2nd ed., Wiley, New York, 1992."},{"key":"R4","doi-asserted-by":"crossref","unstructured":"Y. Pinchover and J. Rubinstein,\n                      An Introduction to Partial Differential Equations\n                      , Cambridge University Press, Cambridge, UK, 2005.","DOI":"10.1017\/CBO9780511801228"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1364\/AO.27.001223"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.21.002164"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1364\/JOSA.73.001434"}],"container-title":["SIAM Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/050645233","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:20:10Z","timestamp":1787232010000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/050645233"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,1]]}},"alternative-id":["10.1137\/050645233"],"URL":"https:\/\/doi.org\/10.1137\/050645233","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,1]]}}}