{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T09:16:30Z","timestamp":1696410990016},"reference-count":15,"publisher":"Wiley","issue":"17-18","license":[{"start":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T00:00:00Z","timestamp":1464739200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/MAT\/04721\/2017\u2010CEAFEL"],"award-info":[{"award-number":["UID\/MAT\/04721\/2017\u2010CEAFEL"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematische Nachrichten"],"published-print":{"date-parts":[[2016,12]]},"abstract":"<jats:p>We give a sharp estimate for the codimension of the poly\u2010Bergman space in the poly\u2010Bergman space over the punctured domain. It is established the behaviour at the infinity point of polyanalytic Bergman functions on the complement of closed disks. In the main result of the paper, we prove that for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mana201500320-math-0001.png\" xlink:title=\"urn:x-wiley:0025584X:media:mana201500320:mana201500320-math-0001\" \/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mana201500320-math-0002.png\" xlink:title=\"urn:x-wiley:0025584X:media:mana201500320:mana201500320-math-0002\" \/> the <jats:italic>j<\/jats:italic>\u2010polyanalytic Bergman space over the domain <jats:italic>U<\/jats:italic> is trivial precisely when the complement of <jats:italic>U<\/jats:italic> has at most one point and at most two points or three points lying in a circle, respectively. We point out the differences between the domains over which the Bergman space and the non\u2010analytic poly\u2010Bergman space are trivial.<\/jats:p>","DOI":"10.1002\/mana.201500320","type":"journal-article","created":{"date-parts":[[2016,6,2]],"date-time":"2016-06-02T01:01:20Z","timestamp":1464829280000},"page":"2273-2280","source":"Crossref","is-referenced-by-count":0,"title":["On the existence of polyanalytic functions"],"prefix":"10.1002","volume":"289","author":[{"given":"Lu\u00eds V.","family":"Pessoa","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Instituto Superior T\u00e9cnico, Universidade de Lisboa Av. Rovisco Pais, 1049 \u2010 001 Lisboa Portugal"}]}],"member":"311","published-online":{"date-parts":[[2016,6]]},"reference":[{"key":"e_1_2_4_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aop.2015.09.009"},{"key":"e_1_2_4_3_1","volume-title":"Trends in Mathematics","author":"Abreu L. 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