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Marek Jarnicki, Peter Pflug Extension of Holomorphic Functions De Gruyter Expositions in Mathematics | Edited by Lev Birbrair, Fortaleza, Brazil Victor P. Maslov, Moscow, Russia Walter D. Neumann, New York City, New York, USA Markus J. Pflaum, Boulder, Colorado, USA Dierk Schleicher, Bremen, Germany Katrin Wendland, Freiburg, Germany Volume 34 Marek Jarnicki, Peter Pflug Extension of Holomorphic Functions | 2nd extended edition Mathematics Subject Classification 2010 32-02, 32Axx, 32Dxx, 32Exx, 32Txx, 32Uxx, 32Wxx Authors Prof. Dr. Marek Jarnicki Faculty of

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De Gruyter Expositions in Mathematics 9 Editors Victor P. Maslov, Moscow, Russia Walter D. Neumann, New York City, New York, USA Invariant Distances and Metrics in Complex Analysis De Gruyter Authors Marek Jarnicki Institute of Mathematics 30-348 Kraków Institute of Mathematics Germany To Mariola and Rosel

(Poland) for the support given during the time we were working on this book (OPUS grant 2015/17/B/ST1/00996). P. S. According to our experience with other books we are sure that a lot of errors can still be found in this text. We appreciate any remark or comment on that which may be sent to one of the e-mail addresses: marek.jarnicki@im.uj.edu.pl peter.pflug@uni-oldenburg.de Kraków–Oldenburg, February 21, 2020. Marek Jarnicki Peter Pflug https://doi.org/10.1515/9783110630275-201

variables. Englewood Cliffs: Pentice-Hall; 1965. [11] Hayman WK, Kennedy PB. Subharmonic functions. San Diego: Academic Press; 1970. [12] Henkin GM, Leiterer J. Theory of functions on complex manifolds. Berlin: Akademie Verlag; 1984. [13] Hörmander L. An introduction to complex analysis in several variables. Amsterdam: North-Holland; 1990. [14] Hörmander L. Notions of convexity. Basel: Birkhäuser; 1994. [15] Jarnicki M, Pflug P. First steps in several complex variables: Reinhardt domains. Zurich: Eur. Math. Soc.; 2008. [16] Jarnicki M, Pflug P. Separately analytic

Analysis 27, 181–212 (2007) / DOI 10.1524/anly.2007.27.2–3.181 c© Oldenbourg Wissenschaftsverlag, München 2007 A general cross theorem with singularities∗ Marek Jarnicki, Peter Pflug Received: May 23, 2006 This paper is dedicated to the memory of our friend and colleague Professor Gerald Schmieder. Summary: We present a general cross theorem for separately holomorphic and meromorphic functions with singularities. 1 Introduction. Main Theorem 1.1 Relative extremal functions Let (Ω, π) be a Riemann region over Cn , i.e. Ω is an n-dimensional complex manifold and π

.M. Voronin 6 Contact Geometry and Linear Differential Equations, V. R. Nazaikinskii, V. E. Shatalov, B. Yu. Sternin 1 Infinite Dimensional Lie Superalgebras, Yu.A.Bahturin, A.A.Mikhalev, V. M. Petrogradsky, M. V. Zaicev 8 Nilpotent Groups and their Automorphisms, E. I. Khukhro Invariant Distances and Metrics in Complex Analysis by Marek Jarnicki Peter Pflug W D E G Walter de Gruyter · Berlin · New York 1993 Authors Marek Jarnicki Instytut Matematyki Uniwersytet Jagiellonski 30-059 Krakow, Poland e-mail: jarnicki@im.uj.edu.pl Peter Pflug Fachbereich Mathematik Universität

. Continuation of L2-holomorphic functions. Math Z. 2004;247:611–7. [173] Jacobson R. Pseudoconvexity is a two-dimensional phenomenon. 2009. arXiv:0907.1304v1. [174] Jarchow H. Locally convex spaces. Stuttgart: Teubner; 1981. [175] Jarnicki M. Holomorphic functions with bounded growth on Riemann domains over ℂn. Zesz Nauk Uniw Jagiell. 1979;20:43–51. [176] Jarnicki M, Pflug P. Non-extendable holomorphic functions of bounded growth in Reinhardt domains. Ann Pol Math. 1985;46:129–40. [177] Jarnicki M, Pflug P. Existence domains of holomorphic functions of restricted growth