Alex Brudnyi

• Fundamental groups of compact Kahler manifolds
• Local inequalities for holomorphic and plurisubharmonic functions
• Limit cycles and the distribution of zeros of families of analytic functions
• Maximal ideals of the space of bounded analytic functions and matrix-valued corona theorem

Book

• Brudnyi, Alex and Brudnyi, Yuri. Methods of Geometric Analysis in Lipschitz extension and trace problems, Volume I Basel: Monographs in Mathematics, Springer, 2011. 560 pps. Print.
• Brudnyi, Alex and Brudnyi, Yuri. Methods of Geometric Analysis in Lipschitz extension and trace problems, Volume II Basel: Monographs in Mathematics, Springer, 2011. 433 pps. Print.
• Brudnyi, Alex. Inequalities for entire functions 15. Bar-Ilan Univ., 2001. 47-66. Print.

Conference Proceedings

• Brudnyi, Alex. Stein-like theory for Banach-valued holomorphic functions on the maximal ideal space of H^\infty and the operator corona problem of Sz.-Nagy 2013.

Journal Article

• Brudnyi, Alex. "A Rolle type theorem for cyclicity of zeros of family of analytic functions". Israel J. Math., 206 (2015): 95-107. Print.
• Brudnyi, Alex. "On the completion problem for algebra H∞". J. Funct. Anal. 266. (2014): 4293-4313. Print.
• Brudnyi, Alex. "Moments finiteness problem and characterization of universal centers of ODEs with analytic coefficients". Nonlinearity 27. (2014): 1611-1631. Print.
• Brudnyi, Alex. "Differential relations on weak Markov sets". C. R. Math. Rep. Acad. Sci. Soc. R. Can. 36. (2014): 1-14. Print.
• Brudnyi, Alex. "Corona problem for H∞ on Riemann surfaces". Fields Institute Communications 72. (2014): 31-45. Print.
• Brudnyi, Alex. "Lq norm inequalities for analytic functions revisited". undefined 179. (2014): 24-32. Print.
• Brudnyi, Alex. "Banach spaces of polynomials as “large” subspaces of l∞-spaces". J. Funct. Anal. 267. (2014): 1285-1290. Print.
• Brudnyi, Alex. "Stein-like theory for Banach-valued holomorphic functions on the maximal ideal space of H∞". Invent. Math. 193.1 (2013): 187-227. Print.
• Brudnyi, Alex. "Holomorphic Banach vector bundles on the maximal ideal space of H∞ and the operator corona problem of Sz.-Nagy". Adv. Math. 232. (2013): 121-141. Print.
• Brudnyi, Alex. "On characterization of universal centers of ODEs with analytic coefficients". C. R. Math. Rep. Acad. Sci. Soc. R. Can. 35.4 (2013): 137-147. Print.
• Brudnyi, Alex. "Composition conditions for classes of analytic functions". Nonlinearity 25. (2012): 3197–3209. Print.
• Brudnyi, Alex. "On the approximation property for Banach spaces predual to H^\infty-spaces". Journal of Functional Analysis 263.9 (2012): 2863–2875. Print.
• Brudnyi, Alex. "Banach-valued holomorphic functions on the maximal ideal space of H^\infty". C. R. Math. Rep. Acad. Sci. Canada 33.4 (2011): 97-106. Print.
• Brudnyi, Alex, Rodman, Leiba and Spitkovsky, Ilya. "Non-denseness of factorable matrix functions". J. Functional Analysis 261.7 (2011): 1969--1991. Print.
• Brudnyi, Alex and Brudnyi, Yuri. "Traces of Ck functions to weak Markov subsets of Rn". St. Petersburg J. Math 23. (2011): 1--19. Print.
• Kinzebulatov, Damir and Brudnyi, Alex. "On holomorphic almost periodic functions on coverings of complex manifolds". New York J. Math 17. (2011): 1--34. Print.
• Brudnyi, Alex, Rodman, Leiba and Spitkovsky, Ilya. "Factorization versus invertibility of matrix functions on compact abelian groups". Operator Theory: Advances and Applications 218. (2011): 225-239. Print.
• Brudnyi, Alex. "On covering numbers of sublevel sets of analytic functions". J. Approx. Theory 162. (2010): 72-93. Print.
• Brudnyi, Alex, Bos, Len and Levenberg, Norm. "On polynomial inequalities on exponential curves in C^n". Constr. Approx. 31.1 (2010): 139-147. Print.
• Brudnyi, Alex and Kinzebulatov, Damir. "Holomorphic semi-almost periodic functions". Integral Equations Operator Theory 66.3 (2010): 293-325. Print.
• Brudnyi, Alex and Kinzebulatov, Damir. "On algebras of holomorphic functions with semi-almost periodic boundary values". C. R. Math. Acad. Sci. Soc. R. Can. 32.1 (2010): 1-12. Print.
• Brudnyi, Alex, Rodman, Leiba and Spitkovsky, Ilya M.. "Projective free algebras of continuous functions on compact abelian groups". J. Funct. Anal. 259.4 (2010): 918-932. Print.
• Brudnyi, Alex and Yomdin, Yosef. "Tree composition condition and moments vanishing". Nonlinearity 23.7 (2010): 1651-1673. Print.
• Brudnyi, Alex. "Some algebraic aspects of the center problem for ordinary differential equations". Qual. Theory Dyn. Syst., 9 (2010): 9--28. Print.
• Brudnyi, Alex. "Holomorphic L^p functions on coverings of strongly pseudoconvex manifolds". Proc. Amer. Math. Soc. 137. (2009): 227-234. Print.
• Brudnyi, Alex and Sasane, Amol. "Sufficient conditions for the projective freeness of Banach algebras". Journal of Functional Analysis 257. (2009): 4003-4014. Print.
• Brudnyi, Alex. "Free subgroups of the group of formal power series and the center problem for ODEs". C. R. Math. Rep. Acad. Sci. Canada 31.4 (2009): 97-106. Print.
• Brudnyi, Alex. "Center problem for ODEs with coefficients generating the group of rectangular paths". C. R. Math. Rep. Acad. Sci. Canada 31.2 (2009): 33-44. Print.
• Brudnyi, Alex. "On local behavior of holomorphic functions along complex submanifolds of C^N". Inventiones Mathematicae 173.2 (2008): 315-363. Print.
• Brudnyi, Alex. "Vanishing of higher-order moments on Lipschitz curves". Bull. sci. Math. 132. (2008): 165-181. Print.
• Brudnyi, Alex. "Formal paths, iterated integrals and the center problem for ODEs". Bull. sci. Math. 132. (2008): 455-485. Print.
• Brudnyi, Alex and Brudnyi, Yuri. "Linear and nonlinear extensions of Lipschitz functions from subsets of metric spaces". St. Petersburg J. Math. 19.3 (2008): 397-406. Print.
• Brudnyi, Alex and Kinzebulatov, Damir. "On uniform subalgebras of L^\infty on the unit circle generated by almost periodic functions". St. Petersburg J. Math. 19.4 (2008): 495-518. Print.
• Brudnyi, Alex. "Hartogs type theorems for CR L^2 functions on coverings of strongly pseudoconvex manifolds". Nagoya Math. J. 189. (2008): 27-47. Print.
• Brudnyi, Alex. "Corona theorem for coverings of Riemann surfaces of finite type". Michigan Math. J. 56. (2008): 283-299. Print.
• Brudnyi, Alex. "An algebraic approach to the center problem for ODEs". Journal of Generalized Lie Theory and Applications 2.3 (2008): 127-132. Print.
• Brudnyi, Alex and Brudnyi, Yuri. "Metric spaces with linear extensions preserving Lipschitz condition". Amer. J. Math. 129. (2007): 217-314. Print.
• Brudnyi, Alex. "On holomorphic functions of slow growth on coverings of strongly pseudoconvex manifolds". J. Funct. Anal. 249.2 (2007): 354-371. Print.
• Brudnyi, Alex. "On holomorphic L^2 functions on coverings of strongly pseudoconvex manifolds". Publications of RIMS, Kyoto University 43. (2007): 963-976. Print.
• Brudnyi, Alex and Brudnyi, Yuri. "A universal Lipschitz extension property for Gromov hyperbolic spaces". Rev. Mat. Iberoamericana 23.3 (2007): 861-896. Print.
• Brudnyi, Alex and Brudnyi, Yuri. "Remez type inequalities and Morrey-Campanato spaces on Ahlfors regular sets". Contemporary Mathematics 445. (2007): 19-44. Print.
• Brudnyi, Alex. "On center sets of ODEs determined by moments of their coefficients". Bull. sci. Math. 130. (2006): 33-48. Print.
• Brudnyi, Alex. "On the center problem for ordinary differential equations". Amer. J. Math. 128.2 (2006): 419-451. Print.
• Brudnyi, Alex. "Representation of holomorphic functions on coverings of pseudoconvex domains in Stein manifolds via integral formulas on these domains". J. Funct. Anal. 231. (2006): 418-437. Print.
• Brudnyi, Alex. "Holomorphic functions of slow growth on coverings of pseudoconvex domains in Stein manifolds". Compositio Math. 142. (2006): 1018-1038. Print.
• Brudnyi, Alex and Brudnyi, Yuri. "Local inequalities for multivariate polynomials and plurisubharmonic functions". In Frontiers in Interpolation and Approximation, (2006): 17-32. Print.
• Brudnyi, Alex. "Hartogs type theorems on coverings of Stein manifolds". Internat. J. Math. 17.3 (2006): 339-349. Print.
• Brudnyi, Alex. "Geometry of Banach spaces predual to H^\infty and corona problem". RIMS Kokyuroku, (2006). Print.
• Brudnyi, Alex and Brudnyi, Yuri. "Extension of Lipschitz functions defined on metric spaces of homogeneous type". Rev. Mat. Complut. 19.2 (2006): 347-359. Print.
• Brudnyi, Alex. "Graphs of zeros of families of analytic functions". Trans. Amer. Math. Soc. 357.5 (2005): 1859-1875. Print.
• Brudnyi, Alex and Brudnyi, Yuri. "Simultaneous Lipschitz extensions". Uspekhi Mat. Nauk 60.6 (2005): 53-72. Print.
• Brudnyi, Alex. "Contractibility of maximal ideal spaces of certain algebras of almost periodic functions". Integral Equations and Operator Theory 52. (2005): 595-598. Print.
• Brudnyi, Alex. "Holomorphic functions of slow growth on coverings of strongly pseudoconvex manifolds". Proc. of Hayama Simpos., (2005). Print.
• Brudnyi, Alex. "Projections in the space H^\infty and the corona theorem for subdomains of coverings of finite bordered Riemann surfaces". Arkiv f\"or Matematik 42.1 (2004): 31-59. Print.
• Brudnyi, Alex. "Grauert- and Lax-Halmos-type theorems and extension of matrices with entries in H^\infty". Journal of Functional Analysis 206.1 (2004): 87-108. Print.
• Brudnyi, Alex. "An explicit expression for the first return map in the center proble". J. Differential Equations 206. (2004): 306-314. Print.
• Brudnyi, Alex. "An algebraic model for the center problem". Bull. sci. Math. 128. (2004): 839-857. Print.
• Brudnyi, Alex. "A uniqueness property for H^infty on coverings of projective manifolds". The Michigan Mathematical Journal 51.3 (2003): 503-507. Print.
• Brudnyi, Alex. "Solvable quotients of K\"ahler groups". The Michigan Mathematical Journal 51.3 (2003): 477-490. Print.
• Brudnyi, Alex. "Solvable matrix representations of K\"ahler groups". Differential Geometry and its Applications 19.2 (2003): 167-191. Print.
• Brudnyi, Alex. "A Jensen inequality for a family of analytic functions and an estimate for the average number of limit cycles". The Bulletin of the London Mathematical Society 35.2 (2003): 229-235. Print.
• Brudnyi, Alex. "Cyclicity of zeros of families of analytic functions". Geometric and Functional Analysis 13.6 (2003): 1161-1188. Print.
• Bos, Len, Brudnyi, Alex, Levenberg, N. and Totik, V.. "Tangential Markov inequalities on transcendental curves". Constructive Approximation. An International Journal for Approximations and Expansions 19.3 (2003): 339-354. Print.
• Brudnyi, Alex. "Topology of the maximal ideal space of H^\infty". Journal of Functional Analysis 189.1 (2002): 21-52. Print.
• Brudnyi, Alex. "The distribution of values of generalized exponential polynomials on convex sets". New Zealand Journal of Mathematics 31.2 (2002): 131-136. Print.
• Brudnyi, Alex. "On a BMO-property for subharmonic functions". The Journal of Fourier Analysis and Applications 8.6 (2002): 603-612. Print.
• Brudnyi, Alex. "Holomorphic functions of exponential growth on abelian coverings of a projective manifold". Compositio Mathematica 127.1 (2001): 69-81. Print.
• Brudnyi, Alex. "Bernstein type inequalities for quasipolynomials". Journal of Approximation Theory 112.1 (2001): 28-43. Print.
• Brudnyi, Alex. "Small amplitude limit cycles and the distribution of zeros of families of analytic functions". Annals of Mathematics. Second Series 154.2 (2001): 227-243. Print.
• Brudnyi, Alex and Onishchik, A. L.. "Triangular de Rham cohomology of compact K\"ahler manifolds". Mat. Sb. 112. (2001): 28-43. Print.
• Brudnyi, Alex. "Matrix-valued corona theorem for multiply connected domains". Indiana University Mathematics Journal 49.4 (2000): 1405-1410. Print.
• Brudnyi, Alex. "On local behavior of analytic functions". Journal of Functional Analysis 169.2 (1999): 481-493. Print.
• Brudnyi, Alex. "Classification theorem for a class of flat connections and representations of K\"ahler groups". The Michigan Mathematical Journal 46.3 (1999): 489-514. Print.
• Brudnyi, Alex. "Cartwright type theorems for a class of plurisubharmonic functions". Indiana University Mathematics Journal 48.2 (1999): 365-384. Print.
• Brudnyi, Alex. "Local inequalities for plurisubharmonic functions". Annals of Mathematics. Second Series 149.2 (1999): 511-533. Print.
• Brudnyi, Alex. "Holomorphic functions of polynomial growth on abelian coverings of a compact complex manifold". Communications in Analysis and Geometry 6.3 (1998): 485-510. Print.
• Brudnyi, Alex. "A Bernstein-type inequality for algebraic functions". Indiana University Mathematics Journal 46.1 (1997): 93-116. Print.
• Brudnyi, Alex. "On Euclidean domains". Communications in Algebra 21.9 (1993): 3327-3336. Print.

Ph.D. Thesis

• Brudnyi, Alex. ∂-bar-equations on compact Kahler manifolds and representations of fundamental groups 1995.