# American Institute of Mathematical Sciences

June  2003, 2(2): 139-145. doi: 10.3934/cpaa.2003.2.139

## A Hilbert space approach to bounded analytic extension in the ball

 1 Department of Mathematics, Ben Gurion University of the Negev, POB 653, Beer Sheva 84105, Israel 2 Department of Mathematics, University of California, Santa Barbara CA 93106, United States 3 Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva 84105, Israel

Received  October 2002 Revised  January 2003 Published  March 2003

One proves, using methods of Hilbert spaces with a reproducing kernel, that any bounded analytic function on a complex curve in general position in the unit ball of C$^n$ extends to a function in the Schur class of the ball.
Citation: Daniel Alpay, Mihai Putinar, Victor Vinnikov. A Hilbert space approach to bounded analytic extension in the ball. Communications on Pure & Applied Analysis, 2003, 2 (2) : 139-145. doi: 10.3934/cpaa.2003.2.139
 [1] Ali Akgül, Mustafa Inc, Esra Karatas. Reproducing kernel functions for difference equations. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1055-1064. doi: 10.3934/dcdss.2015.8.1055 [2] Ali Akgül. A new application of the reproducing kernel method. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020261 [3] Kaitlyn (Voccola) Muller. A reproducing kernel Hilbert space framework for inverse scattering problems within the Born approximation. Inverse Problems & Imaging, 2019, 13 (6) : 1327-1348. doi: 10.3934/ipi.2019058 [4] Ying Lin, Rongrong Lin, Qi Ye. Sparse regularized learning in the reproducing kernel banach spaces with the $\ell^1$ norm. Mathematical Foundations of Computing, 2020, 3 (3) : 205-218. doi: 10.3934/mfc.2020020 [5] Doug Hensley. Continued fractions, Cantor sets, Hausdorff dimension, and transfer operators and their analytic extension. Discrete & Continuous Dynamical Systems - A, 2012, 32 (7) : 2417-2436. doi: 10.3934/dcds.2012.32.2417 [6] Rafael Ortega. Trivial dynamics for a class of analytic homeomorphisms of the plane. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 651-659. doi: 10.3934/dcdsb.2008.10.651 [7] Jaume Llibre, Claudia Valls. Analytic integrability of a class of planar polynomial differential systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2657-2661. doi: 10.3934/dcdsb.2015.20.2657 [8] Stephen Doty and Anthony Giaquinto. Generators and relations for Schur algebras. Electronic Research Announcements, 2001, 7: 54-62. [9] Yiqian Wang. Boundedness of solutions in a class of Duffing equations with a bounded restore force. Discrete & Continuous Dynamical Systems - A, 2006, 14 (4) : 783-800. doi: 10.3934/dcds.2006.14.783 [10] Yuan Guo, Xiaofei Gao, Desheng Li. Structure of the set of bounded solutions for a class of nonautonomous second order differential equations. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1607-1616. doi: 10.3934/cpaa.2010.9.1607 [11] Sandro M. Guzzo, Gabriela Planas. On a class of three dimensional Navier-Stokes equations with bounded delay. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 225-238. doi: 10.3934/dcdsb.2011.16.225 [12] Saman Babaie–Kafaki, Reza Ghanbari. A class of descent four–term extension of the Dai–Liao conjugate gradient method based on the scaled memoryless BFGS update. Journal of Industrial & Management Optimization, 2017, 13 (2) : 649-658. doi: 10.3934/jimo.2016038 [13] Jian Luo, Xueqi Yang, Ye Tian, Wenwen Yu. Corporate and personal credit scoring via fuzzy non-kernel SVM with fuzzy within-class scatter. Journal of Industrial & Management Optimization, 2020, 16 (6) : 2743-2756. doi: 10.3934/jimo.2019078 [14] C. M. Evans, G. L. Findley. Analytic solutions to a class of two-dimensional Lotka-Volterra dynamical systems. Conference Publications, 2001, 2001 (Special) : 137-142. doi: 10.3934/proc.2001.2001.137 [15] Jacek Serafin. A faithful symbolic extension. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1051-1062. doi: 10.3934/cpaa.2012.11.1051 [16] Hans F. Weinberger, Xiao-Qiang Zhao. An extension of the formula for spreading speeds. Mathematical Biosciences & Engineering, 2010, 7 (1) : 187-194. doi: 10.3934/mbe.2010.7.187 [17] Augusto Visintin. An extension of the Fitzpatrick theory. Communications on Pure & Applied Analysis, 2014, 13 (5) : 2039-2058. doi: 10.3934/cpaa.2014.13.2039 [18] Rostislav Grigorchuk, Volodymyr Nekrashevych. Self-similar groups, operator algebras and Schur complement. Journal of Modern Dynamics, 2007, 1 (3) : 323-370. doi: 10.3934/jmd.2007.1.323 [19] Kurt Vinhage. On the rigidity of Weyl chamber flows and Schur multipliers as topological groups. Journal of Modern Dynamics, 2015, 9: 25-49. doi: 10.3934/jmd.2015.9.25 [20] Barry Simon. Zeros of OPUC and long time asymptotics of Schur and related flows. Inverse Problems & Imaging, 2007, 1 (1) : 189-215. doi: 10.3934/ipi.2007.1.189

2019 Impact Factor: 1.105