Interpolation of monogenic functions by using reproducing kernel Hilbert spaces

被引：0

作者：

Cerejeiras, Paula ^{[1
]}

Kaehler, Uwe ^{[1
]}

Legatiuk, Dmitrii ^{[2
]}

机构：

[1] Univ Aveiro, Ctr R&D Math & Applicat, CIDMA, Aveiro, Portugal

[2] Bauhaus Univ Weimar, Appl Math, Weimar, Germany

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 17期

关键词：

Bergman kernel; interpolation; monogenic function; reproducing kernel; sparsity constrain; LINEAR INVERSE PROBLEMS;

D O I：

10.1002/mma.5271

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：8100 / 8114

页数：15

共 50 条

[31] Noncommutative reproducing kernel Hilbert spaces
Ball, Joseph A.
Marx, Gregory
Vinnikov, Victor
JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 271 (07) : 1844 - 1920
[32] RELATIVE REPRODUCING KERNEL HILBERT SPACES
Alpay, Daniel
Jorgensen, Palle
Volok, Dan
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (11) : 3889 - 3895
[33] On reproducing kernel Hilbert spaces of polynomials
Li, XJ
MATHEMATISCHE NACHRICHTEN, 1997, 185 : 115 - 148
[34] On isomorphism of reproducing kernel Hilbert spaces
Napalkov, V. V.
Napalkov, V. V., Jr.
DOKLADY MATHEMATICS, 2017, 95 (03) : 270 - 272
[35] Reproducing kernel Hilbert spaces of CR functions for the Euclidean motion group
Barbieri, D.
Citti, G.
ANALYSIS AND APPLICATIONS, 2015, 13 (03) : 331 - 346
[36] Caratheodory functions on a Riemann surface and associated reproducing kernel Hilbert spaces
Alpay, D
Vinnikov, V
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 333 (06): : 523 - 528
[37] GENERAL SAMPLING THEOREMS FOR FUNCTIONS IN REPRODUCING KERNEL HILBERT-SPACES
NASHED, MZ
WALTER, GG
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 1991, 4 (04) : 363 - 390
[38] The Mittag Leffler reproducing kernel Hilbert spaces of entire and analytic functions
Rosenfeld, Joel A.
Russo, Benjamin
Dixon, Warren E.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 463 (02) : 576 - 592
[39] Probability Error Bounds for Approximation of Functions in Reproducing Kernel Hilbert Spaces
Aydin, Ata Deniz
Gheondea, Aurelian
JOURNAL OF FUNCTION SPACES, 2021, 2021
[40] ON THE OPTIMALITY OF TARGET-DATA-DEPENDENT KERNEL GREEDY INTERPOLATION IN SOBOLEV REPRODUCING KERNEL HILBERT SPACES
Santin, Gabriele
Wenzel, Tizian
Haasdonk, Bernard
SIAM Journal on Numerical Analysis, 2024, 62 (05) : 2249 - 2275

← 1 2 3 4 5 →