TY  - JOUR
AB  - We study the problem of recovering an atomic measure on the unit 2-sphere (Formula presented.) given finitely many moments with respect to spherical harmonics. The analysis relies on the formulation of this problem as an optimization problem on the space of bounded Borel measures on (Formula presented.) as it was considered by Y. de Castro & F. Gamboa (J. Math. Anal. Appl. 395(1):336–354, 2012) and E. Candés & C. Fernandez-Granda (J. Fourier Anal. Appl. 19(6):1229–1254, 2013). We construct a dual certificate using a kernel given in an explicit form and make a concrete analysis of the interpolation problem. Numerical examples are provided and analyzed.
AU  - Filbir, F.
AU  - Schroeder, K.*
AU  - Veselovska, A.*
C1  - 65053
C2  - 52252
SP  - 755-795
TI  - Recovery of atomic measures on the unit sphere.
JO  - Numer. Funct. Anal. Optim.
VL  - 43
IS  - 7
PY  - 2022
SN  - 0163-0563
ER  - 

TY  - JOUR
AU  - Casazza, P.G.*
AU  - Jorgensen, P.E.T.*
AU  - Kornelson, K.A.*
AU  - Kutyniok, G.*
AU  - Larson, D.R.*
AU  - Massopust, P.
AU  - Olafsson, G.*
AU  - Packer, J.A.*
AU  - Silvestrov, S.D.*
AU  - Sun, Q.Y.*
C1  - 8552
C2  - 30305
SP  - 705-707
TI  - Special Issue: Operator algebras and representation theory: Frames, wavelets, and fractals. Preface.
JO  - Numer. Funct. Anal. Optim.
VL  - 33
IS  - 7-9
PB  - Taylor & Francis Inc.
PY  - 2012
SN  - 0163-0563
ER  - 

TY  - JOUR
AB  - We construct univariate periodic splines of complex order and prove multiresolution and localization properties.
AU  - Forster, B.
AU  - Massopust, P.
AU  - Übelacker, T.*
C1  - 8461
C2  - 30111
SP  - 989-1004
TI  - Periodic splines of complex order.
JO  - Numer. Funct. Anal. Optim.
VL  - 33
IS  - 7-9
PB  - Taylor & Francis 
PY  - 2012
SN  - 0163-0563
ER  - 

TY  - JOUR
AB  - We consider approximation methods defined by translates of a positive definite function on a compact group. A characterization of the native space generated by a positive definite function on a compact group is presented. Starting from Bochner's theorem, we construct examples of well-localized positive definite central functions on the rotation group SO(3). Finally, the stability of the interpolation problem and the error analysis for the given examples are studied in detail.
AU  - Erb, W.*
AU  - Filbir, F.
C1  - 105
C2  - 26262
SP  - 1082-1107
TI  - Approximation by positive definite functions on compact groups.
JO  - Numer. Funct. Anal. Optim.
VL  - 29
IS  - 9-10
PB  - Taylor & Francis
PY  - 2008
SN  - 0163-0563
ER  - 

TY  - JOUR
AB  - We consider scattered data approximation problems on SO(3). To this end, we construct a new operator for polynomial approximation on the rotation group. This operator reproduces Wigner-D functions up to a given degree and has uniformly bounded Lp-operator norm for all 1 ? p ? ?. The operator provides a polynomial approximation with the same approximation degree of the best polynomial approximation. Moreover, the operator together with a Markov type inequality for Wigner-D functions enables us to derive scattered data Lp-Marcinkiewicz-Zygmund inequalities for these functions for all 1 ? p ? ?. As a major application of such inequalities, we consider the stability of the weighted least squares approximation problem on SO(3).
AU  - Schmid, D.
C1  - 722
C2  - 25610
SP  - 855-882
TI  - Marcinkiewicz-Zygmund inequalities and polynomial approximation from scattered data on SO(3).
JO  - Numer. Funct. Anal. Optim.
VL  - 29
IS  - 7-8
PB  - Taylor & Francis
PY  - 2008
SN  - 0163-0563
ER  - 

TY  - JOUR
AB  - We present approximation kernels for orthogonal expansions with respect to Bernstein–Szegö polynomials. Theconstruction is derived from known results for Chebyshev polynomials of the first kind and does not pose any restrictions on the Bernstein–Szegö polynomials.
AU  - Hösel, V.*
AU  - Lasser, R.
C1  - 4297
C2  - 23593
SP  - 377-389
TI  - Approximation with Bernstein-Szegö polynomials.
JO  - Numer. Funct. Anal. Optim.
VL  - 27
PY  - 2006
SN  - 0163-0563
ER  -