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

[21] REPRODUCING KERNEL HILBERT SPACES AND PROBABILITY LAW OF RANDOM FUNCTIONS
FORTET, R
[J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1974, 278 (22): : 1439 - 1440
[22] Reproducing Kernel Hilbert Spaces of Polyanalytic Functions of Infinite Order
Alpay, Daniel
Colombo, Fabrizio
Diki, Kamal
Sabadini, Irene
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2022, 94 (04)
[23] Adaptive Decompositions in Monogenic Reproducing Kernel Hilbert Spaces of Paley-Wiener Type
Dang, Pei
Mai, Weixiong
Qian, Tao
[J]. COMPLEX ANALYSIS AND OPERATOR THEORY, 2022, 16 (07)
[24] Generation of point sets by convex optimization for interpolation in reproducing kernel Hilbert spaces
Tanaka, Ken'ichiro
[J]. NUMERICAL ALGORITHMS, 2020, 84 (03) : 1049 - 1079
[25] Sampling expansions and interpolation in unitarily translation invariant reproducing kernel Hilbert spaces
van der Mee, CVM
Nashed, MZ
Seatzu, S
[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2003, 19 (04) : 355 - 372
[26] Sampling Expansions and Interpolation in Unitarily Translation Invariant Reproducing Kernel Hilbert Spaces
Cornelis V.M. van der Mee
M.Z. Nashed
Sebastiano Seatzu
[J]. Advances in Computational Mathematics, 2003, 19 : 355 - 372
[27] Generation of point sets by convex optimization for interpolation in reproducing kernel Hilbert spaces
Ken’ichiro Tanaka
[J]. Numerical Algorithms, 2020, 84 : 1049 - 1079
[28] Noncommutative reproducing kernel Hilbert spaces
Ball, Joseph A.
Marx, Gregory
Vinnikov, Victor
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 271 (07) : 1844 - 1920
[29] Pasting Reproducing Kernel Hilbert Spaces
Sawano, Yoshihiro
[J]. NEW TRENDS IN ANALYSIS AND INTERDISCIPLINARY APPLICATIONS, 2017, : 401 - 407
[30] A Primer on Reproducing Kernel Hilbert Spaces
Manton, Jonathan H.
Amblard, Pierre-Olivier
[J]. FOUNDATIONS AND TRENDS IN SIGNAL PROCESSING, 2014, 8 (1-2): : 1 - 126

← 1 2 3 4 5 →