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Interpolation of monogenic functions by using reproducing kernel Hilbert spaces
Author(s) -
Cerejeiras Paula,
Kähler Uwe,
Legatiuk Dmitrii
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5271
Subject(s) - mathematics , interpolation (computer graphics) , hilbert space , reproducing kernel hilbert space , representer theorem , trilinear interpolation , bilinear interpolation , eigenvalues and eigenvectors , nearest neighbor interpolation , unit sphere , mathematical analysis , kernel (algebra) , trigonometric interpolation , spline interpolation , pure mathematics , kernel method , kernel principal component analysis , computer science , artificial intelligence , statistics , motion (physics) , physics , quantum mechanics , support vector machine
In this paper, we present results on interpolation of monogenic functions in the unit ball of R d + 1using 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.