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Analytic polyhedron
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<h2 id="see-also">See also</h2> <ul><li><a href="/facts/Behnke%25E2%2580%2593Stein_theorem/hY2HnTaN">Behnke–Stein theorem</a></li> <li><a href="/facts/Bergman%25E2%2580%2593Weil_formula/QHfThcV6">Bergman–Weil formula</a></li> <li><a href="/facts/Oka%25E2%2580%2593Weil_theorem/ngtPhkGH">Oka–Weil theorem</a></li></ul> <h2 id="notes">Notes</h2> <ul><li>Åhag, Per; Czyż, Rafał; Lodin, Sam; Wikström, Frank (2007), <a href="http://www.emis.de/journals/UIAM/PDF/45-139-145.pdf">"Plurisubharmonic extension in non-degenerate analytic polyhedra"</a> (PDF), <i>Universitatis Iagellonicae Acta Mathematica</i>, Fasciculus XLV: 139–145, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=2453953">2453953</a>, <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:1176.31010">1176.31010</a>.</li> <li>Khenkin, G. M. (1990), "The Method of Complex Integral Representations in Complex Analysis", in <a href="/facts/Sergey_Nikolsky/fBUR90p3">Vitushkin, A. G.</a> (ed.), <a href="https://archive.org/details/severalcomplexva0000unse/page/19"><i>Several Complex Variables I</i></a>, Encyclopaedia of Mathematical Sciences, vol. 7, Berlin–Heidelberg–New York: <a href="/facts/Springer-Verlag/nAesf6nT">Springer-Verlag</a>, pp. <a href="https://archive.org/details/severalcomplexva0000unse/page/19">19–116</a>, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 3-540-17004-9, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0850491">0850491</a>, <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:0781.32007">0781.32007</a> (also available as <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-387-17004-9).</li> <li><a href="/facts/Robert_Gunning_(mathematician)/gKD3DIq4">Gunning, Robert C.</a>; Rossi, Hugo (1965), <a href="https://books.google.com/books?id=L0zJmamx5AAC"><i>Analytic Functions of Several Complex Variables</i></a>, Prentice–Hall series in Modern Analysis, <a href="/facts/Englewood_Cliffs/gSQUlgvD">Englewood Cliffs</a>, N.J.: <a href="/facts/Prentice-Hall/bynWAuat">Prentice-Hall</a>, pp. xiv+317, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9780821869536, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0180696">0180696</a>, <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:0141.08601">0141.08601</a>.</li> <li><a href="/facts/Robert_Gunning_(mathematician)/gKD3DIq4">Gunning, Robert C.</a> (1990), <i>Introduction to Holomorphic Functions of Several Variables. Volume I: Function Theory</i>, Wadsworth & Brooks/Cole Mathematics Series, <a href="/facts/Belmont%2c_California/yzBQew3N">Belmont, California</a>: Wadsworth & Brooks/Cole, pp. xx+203, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-534-13308-8, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=1052649">1052649</a>, <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:0699.32001">0699.32001</a>.</li> <li><a href="/facts/Lars_H%25C3%25B6rmander/mxyNnmRA">Hörmander, Lars</a> (1990) [1966], <i>An Introduction to Complex Analysis in Several Variables</i>, North–Holland Mathematical Library, vol. 7 (3rd (Revised) ed.), Amsterdam–London–New York–Tokyo: <a href="/facts/Elsevier/jkPSAEmR">North-Holland</a>, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-444-88446-7, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=1045639">1045639</a>, <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:0685.32001">0685.32001</a>.</li> <li>Kaup, Ludger; Kaup, Burchard (1983), <a href="https://books.google.com/books?id=nDgBsOurnAIC"><i>Holomorphic functions of several variables</i></a>, de Gruyter Studies in Mathematics, vol. 3, Berlin–New York: <a href="/facts/Walter_de_Gruyter/2wJSEv3m">Walter de Gruyter</a>, pp. XV+349, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-3-11-004150-7, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0716497">0716497</a>, <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:0528.32001">0528.32001</a>.</li> <li><a href="/facts/Francesco_Severi/LRqMFxVM">Severi, Francesco</a> (1958), <i>Lezioni sulle funzioni analitiche di più variabili complesse – Tenute nel 1956–57 all'Istituto Nazionale di Alta Matematica in Roma</i> (in Italian), Padova: CEDAM – Casa Editrice Dott. Antonio Milani, pp. XIV+255, <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:0094.28002">0094.28002</a>. Notes from a course held by Francesco Severi at the <a href="/facts/Istituto_Nazionale_di_Alta_Matematica/u9kyPs1e">Istituto Nazionale di Alta Matematica</a> (which at present bears his name), containing appendices of Enzo Martinelli, Giovanni Battista Rizza and Mario Benedicty. An English translation of the title reads as:-"<i>Lectures on analytic functions of several complex variables – Lectured in 1956–57 at the Istituto Nazionale di Alta Matematica in Rome</i>".</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>See (Åhag et al. 2007, p. 139) and (Khenkin 1990, p. 35). - Åhag, Per; Czyż, Rafał; Lodin, Sam; Wikström, Frank (2007), "Plurisubharmonic extension in non-degenerate analytic polyhedra" (PDF), Universitatis Iagellonicae Acta Mathematica, Fasciculus XLV: 139–145, MR 2453953, Zbl 1176.31010 <a href="http://www.emis.de/journals/UIAM/PDF/45-139-145.pdf" target="_blank">http://www.emis.de/journals/UIAM/PDF/45-139-145.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>(Khenkin 1990, pp. 35–36). - Khenkin, G. M. (1990), "The Method of Complex Integral Representations in Complex Analysis", in Vitushkin, A. G. (ed.), Several Complex Variables I, Encyclopaedia of Mathematical Sciences, vol. 7, Berlin–Heidelberg–New York: Springer-Verlag, pp. 19–116, ISBN 3-540-17004-9, MR 0850491, Zbl 0781.32007 <a href="https://archive.org/details/severalcomplexva0000unse/page/19" target="_blank">https://archive.org/details/severalcomplexva0000unse/page/19</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> </ol>