Interpolation of monogenic functions by using reproducing kernel Hilbert spaces
In this paper, we present results on interpolation of monogenic functions in the unit ball of Rd+1 using reproducing kernels and randomly chosen interpolation points. The main theoretical results are proved based on the concept of uniformly discrete sequences. Furthermore, estimates for the interpol...
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| Published in: | Mathematical methods in the applied sciences Vol. 41; no. 17; pp. 8100 - 8114 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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| Abstract | In this paper, we present results on interpolation of monogenic functions in the unit ball of
Rd+1 using reproducing kernels and randomly chosen interpolation points. The main theoretical results are proved based on the concept of uniformly discrete sequences. Furthermore, estimates for the interpolation error as well as for the eigenvalues of the interpolation problems are presented. Numerical results are presented in the end. |
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| AbstractList | In this paper, we present results on interpolation of monogenic functions in the unit ball of
Rd+1 using reproducing kernels and randomly chosen interpolation points. The main theoretical results are proved based on the concept of uniformly discrete sequences. Furthermore, estimates for the interpolation error as well as for the eigenvalues of the interpolation problems are presented. Numerical results are presented in the end. In this paper, we present results on interpolation of monogenic functions in the unit ball of Rd+1 using reproducing kernels and randomly chosen interpolation points. The main theoretical results are proved based on the concept of uniformly discrete sequences. Furthermore, estimates for the interpolation error as well as for the eigenvalues of the interpolation problems are presented. Numerical results are presented in the end. In this paper, we present results on interpolation of monogenic functions in the unit ball of using reproducing kernels and randomly chosen interpolation points. The main theoretical results are proved based on the concept of uniformly discrete sequences. Furthermore, estimates for the interpolation error as well as for the eigenvalues of the interpolation problems are presented. Numerical results are presented in the end. |
| Author | Cerejeiras, Paula Legatiuk, Dmitrii Kähler, Uwe |
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| Cites_doi | 10.1515/9783112576182 10.1090/S0002-9947-06-04064-5 10.1137/0722066 10.1002/cpa.20042 10.1016/j.acha.2006.05.003 10.1016/j.jfa.2004.07.012 10.1080/17476933.2016.1250896 10.1007/978-1-4612-4814-9 10.1016/j.acha.2004.12.004 10.1007/s00041-011-9169-2 10.1016/S0252-9602(14)60035-7 10.1016/j.jmaa.2014.07.028 10.1088/0266-5611/26/2/025007 10.1007/978-3-0348-0667-1_14 10.1016/j.cam.2016.08.002 10.3934/ipi.2007.1.29 10.1088/0266-5611/24/6/065013 10.1016/S1076-5670(07)00001-8 10.1007/978-3-319-42514-6 10.1109/IJCNN.2009.5179093 |
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| References | 2017; 62 2015; 421 2000; 42 2006; 7 1975 2011; 17 1985; 22 2017; 311 14 2005; 19 2010; 26 2007; 359 2005; 221 2014; 34B 2004; 57 1987 2008; 24 2016 2015 1982 2013 2012; 7 2007; 1 2007; 22 1989 2008; 150 e_1_2_8_28_1 e_1_2_8_24_1 e_1_2_8_25_1 e_1_2_8_26_1 Davis PJ (e_1_2_8_2_1) 1975 e_1_2_8_27_1 Qaisar S (e_1_2_8_22_1) 2012; 7 Gürlebeck K (e_1_2_8_10_1) 1989 Micchelli CA (e_1_2_8_12_1) 2006; 7 Schuster A (e_1_2_8_17_1) 2000; 42 e_1_2_8_3_1 e_1_2_8_5_1 e_1_2_8_4_1 e_1_2_8_7_1 e_1_2_8_6_1 e_1_2_8_9_1 e_1_2_8_8_1 e_1_2_8_20_1 e_1_2_8_21_1 e_1_2_8_23_1 e_1_2_8_18_1 e_1_2_8_19_1 e_1_2_8_13_1 e_1_2_8_15_1 Brackx F (e_1_2_8_14_1) 1982 e_1_2_8_16_1 Daubechies I (e_1_2_8_29_1); 14 e_1_2_8_11_1 e_1_2_8_30_1 |
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| Snippet | In this paper, we present results on interpolation of monogenic functions in the unit ball of
Rd+1 using reproducing kernels and randomly chosen interpolation... In this paper, we present results on interpolation of monogenic functions in the unit ball of using reproducing kernels and randomly chosen interpolation... In this paper, we present results on interpolation of monogenic functions in the unit ball of Rd+1 using reproducing kernels and randomly chosen interpolation... |
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| SubjectTerms | Bergman kernel Eigenvalues Hilbert space Interpolation monogenic function reproducing kernel sparsity constrain |
| Title | Interpolation of monogenic functions by using reproducing kernel Hilbert spaces |
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