TY - JOUR UR - http://lib.ugent.be/catalog/pug01:1084573 ID - pug01:1084573 LA - eng TI - Basics of a generalized Wiman-Valiron theory for monogenic Taylor series of finite convergence radius PY - 2010 JO - (2010) MATHEMATISCHE ZEITSCHRIFT SN - 0025-5874 PB - 2010 AU - Constales, Denis TW16 801000631668 0000-0002-6826-6185 AU - De Almeida, R AU - Krausshar, RS AB - In this paper, we develop the basic concepts for a generalized Wiman-Valiron theory for Clifford algebra valued functions that satisfy inside an n + 1-dimensional ball the higher dimensional Cauchy-Riemann system . These functions are called monogenic or Clifford holomorphic inside the ball. We introduce growth orders, the maximum term and a generalization of the central index for monogenic Taylor series of finite convergence radius. Our goal is to establish explicit relations between these entities in order to estimate the asymptotic growth behavior of a monogenic function in a ball in terms of its Taylor coefficients. Furthermore, we exhibit a relation between the growth order of such a function f and the growth order of its partial derivatives. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 1084573 | ||
005 | 20180813140532.0 | ||
008 | 101207s2010------------------------eng-- | ||
022 | a 0025-5874 | ||
024 | a 000281725600009 2 wos | ||
024 | a 1854/LU-1084573 2 handle | ||
024 | a 10.1007/s00209-009-0592-x 2 doi | ||
040 | a UGent | ||
245 | a Basics of a generalized Wiman-Valiron theory for monogenic Taylor series of finite convergence radius | ||
260 | c 2010 | ||
520 | a In this paper, we develop the basic concepts for a generalized Wiman-Valiron theory for Clifford algebra valued functions that satisfy inside an n + 1-dimensional ball the higher dimensional Cauchy-Riemann system . These functions are called monogenic or Clifford holomorphic inside the ball. We introduce growth orders, the maximum term and a generalization of the central index for monogenic Taylor series of finite convergence radius. Our goal is to establish explicit relations between these entities in order to estimate the asymptotic growth behavior of a monogenic function in a ball in terms of its Taylor coefficients. Furthermore, we exhibit a relation between the growth order of such a function f and the growth order of its partial derivatives. | ||
598 | a A1 | ||
700 | a Constales, Denis u TW16 0 801000631668 0 0000-0002-6826-6185 9 F43DD0B8-F0ED-11E1-A9DE-61C894A0A6B4 | ||
700 | a De Almeida, R | ||
700 | a Krausshar, RS | ||
650 | a Mathematics and Statistics | ||
653 | a ORDER | ||
653 | a GROWTH | ||
773 | t MATHEMATISCHE ZEITSCHRIFT g Math. Z. 2010. 266 (3) p.665-681 q 266:3<665 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/1084573/file/1085430 z [ugent] y Constales_2010_MZ_266_3_665.pdf | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/1084573/file/1085008 z [open] y drsBall5.pdf | ||
920 | a article | ||
Z30 | x EA 1 TW16 | ||
922 | a UGENT-EA |
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