Professor GABRIELA KOHR – A life for research. In memoriam
Keywords:
Gabriela Kohr, geometric function theory of one and several complex variables, Loewner theory, mappings with parametric representation, extension operator, complex analysis.Abstract
We review the main contributions of Professor Gabriela Kohr in her studies in the Geometric function theory in several complex variables and complex Banach spaces with special emphasis on the theory of Loewner chains and the Loewner differential equation.
Mathematics Subject Classification (2010): 32A18, 32A30, 32K05, 30C45, 30C80, 30D45.
References
Anders´en, E., Lempert, L., On the group of holomorphic automorphisms of Cn, Invent. Math., 110(1992), 371-388.
Arosio, L., Bracci, F., Hamada, H., Kohr, G., An abstract approach to Loewner chains, J. Anal. Math., 119(2013), 89-114.
Bracci, F., Shearing process and an example of a bounded support function in S0(B2), Comput. Methods Funct. Theory, 15(2015), 151-157.
Bracci, F., Graham, I., Hamada, H., Kohr, G., Variation of Loewner chains, extreme and support points in the class S0 in higher dimensions, Constr. Approx., 43(2016), 231-251.
Chu, C.-H., Hamada, H., Honda, T., Kohr, G., Distortion of locally biholomorphic Bloch mappings on bounded symmetric domains, J. Math. Anal. Appl., 441(2016), 830-843.
Chu, C.-H., Hamada, H., Honda, T., Kohr, G., Bloch functions on bounded symmetric domains, J. Funct. Anal., 272(2017), 2412-2441.
Chu, C.-H., Hamada, H., Honda, T., Kohr, G., Bloch space of a bounded symmetric domain and composition operators, Complex Anal. Oper. Theory, 13(2019), 479-492.
Chuaqui, M., Hamada, H., Hern´andez, R., Kohr, G., Pluriharmonic mappings and linearly connected domains in Cn, Israel J. Math., 200(2014), 489-506.
Curt, P., Kohr, G., Subordination chains and Loewner differential equations in several complex variables, Ann. Univ. Mariae-Curie Sklodowska, LVII(2003), 35-43.
Curt, P., Kohr, G., Some remarks concerning quasiconformal extensions in several complex variables, J. Inequal. Appl., Vol. 2008, Article ID 690932, 16 pp.
Duren, P., Graham, I., Hamada, H., Kohr, G., Solutions for the generalized Loewner differential equation in several complex variables, Math. Ann., 347(2010), 411-435.
Duren, P., Hamada, H., Kohr, G., Two-point distortion theorems for univalent harmonic and pluriharmonic mappings, Trans. Amer. Math. Soc., 363(2011), 6197-6218.
Elin, M., Shoikhet, D., Sugawa, T., Geometric properties of the nonlinear resolvent of holomorphic generators, J. Math. Anal. Appl., 483(2020), 1-18.
Fornaess, J.E., Wold, E.F., An embedding of the unit ball that does not embed into a Loewner chain, Math. Z., 296(2020), 73-78.
Graham, I., Hamada, H., Honda, T., Kohr, G., Shon, K.H., Growth, distortion and coefficient bounds for Carath´eeodory families in Cn and complex Banach spaces, J. Math. Anal. Appl., 416(2014), 449-469.
Graham, I., Hamada, H., Kohr, G., Parametric representation of univalent mappings in several complex variables, Canad. J. Math., 54(2002), 324-351.
Graham, I., Hamada, H., Kohr, G., Extension operators and subordination chains, J. Math. Anal. Appl., 386(2012), 278-289.
Graham, I., Hamada, H., Kohr, G., Extremal problems for mappings with g-parametric representation on the unit polydisc in Cn, In: Agranovsky M., Golberg A., Jacobzon F., Shoikhet D., Zalcman L. (eds.), Complex Analysis and Dynamical Systems, 141-167, Trends Math., Birkha¨user/Springer, Cham, 2018.
Graham, I., Hamada, H., Kohr, G., A Schwarz lemma at the boundary on complex Hilbert balls and applications to starlike mappings, J. Anal. Math., 140(2020), 31-53.
Graham, I., Hamada, H., Kohr, G., Loewner chains, Bloch mappings and Pfaltzgraff- Suffridge extension operators on bounded symmetric domains, Complex Var. Elliptic Equ., 65(2020), 57-73.
Graham, I., Hamada, H., Kohr, G., Loewner chains and nonlinear resolvents of the Carath´eodory family on the unit ball in Cn, J. Math. Anal. Appl., 491(2020), 124289.
Graham, I., Hamada, H., Kohr, G., Kohr, M., Asymptotically spirallike mappings in several complex variables, J. Anal. Math., 105(2008), 267-302.
Graham, I., Hamada, H., Kohr, G., Kohr, M., Parametric representation and asymptotic starlikeness in Cn, Proc. Amer. Math. Soc., 136(2008), 3963-3973.
Graham, I., Hamada, H., Kohr, G., Kohr, M., Spirallike mappings and univalent subordination chains in Cn, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 7(2008), 717-740.
Graham, I., Hamada, H., Kohr, G., Kohr, M., Extremal properties associated with univalent subordination chains in Cn, Math. Ann., 359(2014), 61-99.
Graham, I., Hamada, H., Kohr, G., Kohr, M., Support points and extreme points for mappings with A-parametric representation in Cn, J. Geom. Anal., 26(2016), 1560-1595.
Graham, I., Hamada, H., Kohr, G., Kohr, M., Bounded support points for mappings with g-parametric representation in C2, J. Math. Anal. Appl., 454(2017), 1085-1105.
Graham, I., Hamada, H., Kohr, G., Kohr, M., g-Loewner chains, Bloch functions and extension operators in complex Banach spaces, Analysis and Mathematical Physics, 10(2020), no. 1, Art. 5, 28 pp.
Graham, I., Hamada, H., Kohr, G., Pfaltzgraff, J.A., Convex subordination chains in several complex variables, Canadian J. Math., 61(2009), 566-582.
Graham, I., Hamada, H., Kohr, G., Suffridge, T.J., Extension operators for locally univalent mappings, Michigan Math. J., 50(2002), 37-55.
Graham, I., Kohr, G., Univalent mappings associated with the Roper-Suffridge extension operator, J. Analyse Math., 81(2000), 331-342.
Graham, I., Kohr, G., Geometric Function Theory in One and Higher Dimensions, Marcel Dekker, New York, 2003.
Graham, I., Kohr, G., Kohr, M., Loewner chains and parametric representation in several complex variables, J. Math. Anal. Appl., 281(2003), 425-438.
Graham, I., Kohr, G., Kohr, M., Loewner chains and the Roper-Suffridge extension operator, J. Math. Anal. Appl., 247(2000), 448-465.
Graham, I., Kohr, G., Pfaltzgraff, J.A., The general solution of the Loewner differential equation on the unit ball in Cn, Contemporary Math. (AMS), 382 (2005), American Math. Soc., Providence, RI, 191-203.
Hamada, H., Approximation properties on spirallike domains of Cn, Adv. Math., 268(2015), 467-477.
Hamada, H., A Schwarz lemma at the boundary using the Julia-Wolff-Carath´eodory type condition on finite dimensional irreducible bounded symmetric domains, J. Math. Anal. Appl., 465(2018), 196-210.
Hamada, H., Honda, T., Kohr, G., Trace-order and a distortion theorem for linearly invariant families on the unit ball of a finite dimensional JB∗-triple, J. Math. Anal. Appl., 396(2012), 829-843.
Hamada, H., Iancu, M., Kohr, G., Convergence results for families of univalent mappings on the unit ball in Cn, Ann. Acad. Sci. Fenn. Math., 41(2016), 601-616.
Hamada, H., Iancu, M., Kohr, G., Approximation of univalent mappings by automorphisms and quasiconformal diffeomorphisms in Cn, J. Approx. Theory., 240(2019), 129-144.
Hamada, H., Iancu, M., Kohr, G., Spiralshapelike mappings in several complex variables, Ann. Mat. Pura Appl., 199(2020), 2181-2195.
Hamada, H., Iancu, M., Kohr, G., Schleißinger, S., Approximation properties of univalent mappings on the unit ball in Cn J. Approx. Theory, 226(2018), 14-33.
Hamada, H., Kohr, G., Quasiconformal extension of biholomorphic mappings in several complex variables, J. Analyse Math., 96(2005), 269-282.
Hamada, H., Kohr, G., Univalence criterion and quasiconformal extension of holomorphic mappings, Manuscripta Math., 141(2013), 195-209.
Hamada, H., Kohr, G., Pluriharmonic mappings in Cn and complex Banach spaces, J. Math. Anal. Appl., 426(2015), 635-658.
Hamada, H., Kohr, G., α-Bloch mappings on bounded symmetric domains in Cn, Com- plex Anal. Oper. Theory, 12(2018), 509-527.
Hamada, H., Kohr, G., Support points for families of univalent mappings on bounded symmetric domains, Sci. China Math., 63(2020), 2379-2398.
Hamada, H., Kohr, G., A boundary Schwarz lemma for mappings from the unit polydisc to irreducible bounded symmetric domains, Math. Nachr., 293(2020), 1345-1351.
Hamada, H., Kohr, G., A rigidity theorem at the boundary for holomorphic mappings with values in finite dimensional bounded symmetric domains, Math. Nachr., 294(2021), 2151-2159.
Hamada, H., Kohr, G., Kohr, M., The Fekete-Szeg¨o problem for starlike mappings and nonlinear resolvents of the Carath´eodory family on the unit balls of complex Banach spaces, Anal. Math. Phys., 11(2021), no. 3, Paper No. 115.
Hamada, H., Kohr, G., Mocanu, P.T., S¸erb, I., Convex subordination chains and injective mappings in Cn, J. Math. Anal. Appl., 364(2010), 32-40.
Hamada, H., Kohr, G., Muir Jr., J.R., Extensions of Ld-Loewner chains to higher dimensions, J. Anal. Math., 120(2013), 357-392.
Kohr, G., On some distortion results for convex mappings in Cn, Complex Variables Theory Appl., 39(1999), 161-175.
Kohr, G., Basic Topics in Holomorphic Functions of Several Complex Variables, Cluj University Press, 2003.
Kohr, G., Loewner chains and a modification of the Roper-Suffridge extension operator, Mathematica (Cluj), 71(2006), 41-48.
Kohr, G., http://math.ubbcluj.ro/∼gkohr/
Kohr, G., Liczberski, P., Univalent Mappings of Several Complex Variables, Cluj University Press, 1998.
Kohr, G., Mocanu, P.T., Special Chapters of Complex Analysis, Cluj University Press, 2005 (in Romanian).
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