{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T15:22:30Z","timestamp":1764688950665},"reference-count":13,"publisher":"Wiley","issue":"17-18","license":[{"start":{"date-parts":[[2013,8,15]],"date-time":"2013-08-15T00:00:00Z","timestamp":1376524800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematische Nachrichten"],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:p>If <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mana201010057-math-0001.png\" xlink:title=\"urn:x-wiley:0025584X:mana201010057:equation:mana201010057-math-0001\" \/>, is an increasing sequence (well ordered by inclusion) of domains then the sequence of poly\u2010Bergman projections on the domains <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mana201010057-math-0002.png\" xlink:title=\"urn:x-wiley:0025584X:mana201010057:equation:mana201010057-math-0002\" \/> strongly converges to the poly\u2010Bergman projection on the limit domain. As a corollary some properties of the poly\u2010Bergman spaces on the half\u2010planes are deduced from the corresponding ones in the unit disk. We obtain explicit representation of the poly\u2010Bergman projections in terms of the two\u2010dimensional singular integral operators <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mana201010057-math-0003.png\" xlink:title=\"urn:x-wiley:0025584X:mana201010057:equation:mana201010057-math-0003\" \/>, likewise explicit formulas for the poly\u2010Bergman kernels. We prove that the poly\u2010Bergman projections on the sectors with a non\u2010smooth boundary do not admit the usual representations by the two\u2010dimensional singular integral operators. The variation of the domain and the latter peculiarity of the poly\u2010Bergman projections allow us to furnish a larger class of domains not admitting Dzhuraev's formulas.<\/jats:p>","DOI":"10.1002\/mana.201010057","type":"journal-article","created":{"date-parts":[[2013,8,15]],"date-time":"2013-08-15T15:19:24Z","timestamp":1376579964000},"page":"1850-1862","source":"Crossref","is-referenced-by-count":9,"title":["The method of variation of the domain for poly\u2010Bergman spaces"],"prefix":"10.1002","volume":"286","author":[{"given":"Lu\u00eds V.","family":"Pessoa","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e1tica Universidade T\u00e9cnica de Lisboa \u2010 Instituto Superior T\u00e9cnico, Av. Rovisco Pais  1049 \u2010 001 Lisboa Portugal"}]}],"member":"311","published-online":{"date-parts":[[2013,8,15]]},"reference":[{"key":"e_1_2_5_2_1","volume-title":"Polyanalytic Functions","author":"Balk M. 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