{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T22:48:55Z","timestamp":1767912535255,"version":"3.49.0"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Z. Anal. Anwend."],"published-print":{"date-parts":[[1996,6,30]]},"abstract":"<jats:p>\n                    The\n                    <jats:inline-formula>\n                      <jats:tex-math>\\Pi<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -operator plays a mayor role in complex analysis, especially in the theory of generalized analytic functions in the sense of Vekua. The present paper deals with a hyper-complex generalization of the complex\n                    <jats:inline-formula>\n                      <jats:tex-math>\\Pi<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -operator which turns out to have most of the useful properties of its complex origin such as mapping properties and invertibility. At the end an application of the generalized\n                    <jats:inline-formula>\n                      <jats:tex-math>\\Pi<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -operator to the solution of a hypercomplex Beltrami equation will be studied.\n                  <\/jats:p>","DOI":"10.4171\/zaa\/700","type":"journal-article","created":{"date-parts":[[2013,9,2]],"date-time":"2013-09-02T04:28:44Z","timestamp":1378096124000},"page":"283-297","source":"Crossref","is-referenced-by-count":11,"title":["On a Spatial Generalization of the Complex $\\Pi$-Operator"],"prefix":"10.4171","volume":"15","author":[{"given":"Klaus","family":"G\u00fcrlebeck","sequence":"first","affiliation":[{"name":"Bauhaus-Universit\u00e4t Weimar, Germany"}]},{"given":"Uwe","family":"K\u00e4hler","sequence":"additional","affiliation":[{"name":"Universidade de Aveiro, Portugal"}]}],"member":"2673","container-title":["Zeitschrift f\u00fcr Analysis und ihre Anwendungen"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/ZAA\/700","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T14:02:50Z","timestamp":1762956170000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/zaa\/700"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,6,30]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.4171\/zaa\/700","relation":{},"ISSN":["0232-2064","1661-4534"],"issn-type":[{"value":"0232-2064","type":"print"},{"value":"1661-4534","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,6,30]]}}}