- Putatively optimal projective spherical designs with little apparent symmetry

- An explicit construction of the unitarily
invariant quaternionic polynomial spaces on
the sphere

- Complex spherical designs from group orbits

*J. Approx. Theory***xxx**(2024), no. x, xxx-xxx. - On Waldron Interpolation on a Simplex in R^d

- Equations for the overlaps of a SIC

- Constructing high order spherical designs as a union of two of lower order

- Testing isomorphism between tuples of subspaces

- A variational characterisation of projective spherical designs over the quaternions

- Multivariate Lagrange interpolation and polynomials of one quaternionic variable

*Dolomites Research Notes on Approximation***17**(2024), 20-27. - Tight frames over the quaternions and equiangular lines

- Extremal growth of polynomials

*Anal. Math. 46***no. 2**(2020), 195-224. - SICs and the elements of order three in the Clifford group

*J. Phys. A***52, no. 10**(2019), 1-31. - Spherical (t,t)-designs with a small number of vectors

*Linear Algebra Appl.***608**(2021), 84-106. - The Fourier transform of a projective group frame

*Appl. Comput. Harmon. Anal.***49, no. 1**(2020), 74-98. - An introduction to finite tight frames

*Applied and Computational Harmonic Analysis*,*Birhauser*, 2018. - Constructing exact symmetric informationally complete measurements from numerical solutions

*J. Phys. A***51, no. 16**(2018), 40 pp. - On the number of harmonic frames

*Appl. Comput. Harmon. Anal.***48**(2020), 46-63. - A sharpening of the Welch bounds and the existence of real and complex spherical t-designs

*IEEE Trans. Info. Theory***63**(2017), no. 11, 6849-6857. - The construction of G-invariant finite tight frames

*J. Fourier Anal. Appl.***22**(2016), no. 5, 1097-1120. - Tight frames for cyclotomotic fields and other rational vector spaces

*Linear Algebra Appl.***476**(2015), 98-123. - Nice error frames, canonical abstract error groups and the construction of SICs

*Linear Algebra Appl.***516**(2017), 93-117. - The projective symmetry group of a finite frame

*New Zealand J. Math.***48**(2018), 55-81. - A characterisation of projective unitary equivalence of
finite frames

*SIAM J. Discrete Math.***30**(2016), no. 2, 976-994. - Multivariate Bernstein operators and redundant systems

*J. Approx. Theory***192**(2015), 215-233. - Group frames

chapter in the book*Finite frames*(edited by G. Kutyniok and P. Casazza), Springer 2013. - On the construction of highly symmetric tight frames and complex polytopes

*Linear Algebra Appl.***439**(2013), no. x, 4135-4151. - Frames for vector spaces and affine spaces

*Linear Algebra Appl.***435**(2011), no. 1, 77-94. - Affine generalised barycentric coordinates

*Jaen J. Approx.***3**(2011), no. 2, 209-226. - A classification of the harmonic frames up to unitary equivalence

*Appl. Comput. Harmon. Anal.***30**(2011), 307-318. - The symmetry group of a finite frame

*Linear Algebra Appl.***433**(2010), no. 1, 248-262. - Recursive three term recurrence relations for the Jacobi polynomials on a triangle

*Constr. Approx.***33**(2011), no. 3, 405-424. - On the construction of equiangular frames from graphs

*Linear Algebra Appl.***431**(2009), no. 11, 2228-2242. - On the convergence of optimal measures

*Constr. Approx.***32**(2010), no. 1, 159-179. - Increasing the polynomial reproduction of a quasi-interpolation operator

*J. Approx. Theory***161**(2009), 114-126. - On the spacing of Fekete points for a sphere, ball or simplex

*Indag. Math.***19**(2008), no. 2, 163-176. - Continuous and discrete tight frames of orthogonal polynomials for a radially symmetric weight

*Constr. Approx.***30**(2009), no. 1, 33-52. - On the Vandermonde determinant of Padua-like points

*Dolomites Research Notes on Approximation***2**(2009), 1-15. - Tight frames generated by finite nonabelian groups

*Numer. Algorithms***48**, (2008), 11-28. - Scattered data interpolation by box splines

*AMS/IP Studies in Advanced Mathematics***42**(2008), 749-767. - Some remarks on Heisenberg frames and sets of equiangular lines

*New Zealand J. Math.***36**(2007), 113-137. - Orthogonal polynomials on the disc

*J. Approx. Theory***150**(2008), no. 2, 117-131. - Hermite polynomials on the plane

*Numer. Algorithms***45**(2007), 231-238. - Multivariate Jacobi polynomials with singular weights

*East J. Approx.***13**(2007), no. 2, 163-183. - Computing orthogonal polynomials on a triangle by degree raising

*Numer. Algorithms***42**, (2006), 171-179. - On computing all harmonic frames of $n$ vectors in $\C^d$

*Appl. Comput. Harmon. Anal.***21**(2006), 168-181. - On the Bernstein-Bézier form of Jacobi polynomials on a simplex

*J. Approx. Theory***140**(2006), no. 1, 86-99. - Pseudometrics, distances and multivariate polynomial inequalities

*J. Approx. Theory***153**(2008), no. 1, 80--96. - Tight frames and their symmetries

*Const. Approx.***21**(2005), no. 1, 83-112. - The vertices of the platonic solids are tight frames

*Advances in Constructive Approximation: Vanderbilt 2003*, 495-498, (edited by M. Neamtu and E. B. Saff), Nashboro Press, 2004. - Metrics associated to multivariate polynomial inequalities

*Advances in Constructive Approximation: Vanderbilt 2003*, 133-147, (edited by M. Neamtu and E. B. Saff), Nashboro Press, 2004. - A generalised beta integral and the limit of the Bernstein-Durrmeyer operator with Jacobi weights

*J. Approx. Theory***122**(2003), no. 1, 141-150. - Generalised Welch Bound Equality sequences are tight frames

*IEEE Trans. Info. Theory***49**(2003), no. 9, 2307-2309. - The diagonalisation of the multivariate Bernstein operator

*J. Approx. Theory***117**(2002), no. 1, 103-131. - Isometric tight frames

*Electronic Journal of Linear Algebra***9**(2002), 122-128. - On the structure of Kergin interpolation for points in general position

*Recent Progress in Multivariate Approximation*, 75-88 (edited by W. Haußmann, K. Jetter and M. Reimer), International Series of Numerical Mathematics 137, Birkhauser, Basel, 2001. - Signed frames and Hadamard products of Gram matrices

*Linear Algebra Appl.***347**(2002), no. 1-3, 131-157. - Extremising the $L_p$-norm of a monic polynomial with roots in a given interval and Hermite interpolation

*East J. Approx.***3**(2001), no. 3, 255-266. - The eigenstructure of the Bernstein operator

*J. Approx. Theory***105**(2000), no. 1, 133-165. - Mean value interpolation for points in general position
- Inverse and direct theorems for best uniform approximation by polynomials
- On Bernstein's comparison theorem, Peano kernels of constant sign and near-minimax approximation
- Minimally supported error representations and approximation by the constants

*Numer. Math.***85**(2000), no. 3, 469--484. - Refinements of the Peano kernel theorem

*Numer. Funct. Anal. Optim.***20**(1999), no. 1-2, 147--161. - Sharp error estimates for multivariate positive linear operators which reproduce the linear polynomials

*Approximation Theory IX - Vol. 1*, 339--346, (edited by C. K. Chui and L. L. Schumaker), Vanderbilt University Press, 1998. - Multipoint Taylor formulae

*Numer. Math.***80**(1998), no. 3, 461-494. - The error in linear interpolation at the vertices of a simplex

*SIAM J. Numer. Anal.***35**(1998), no. 3, 1191-1200.- and some related open problems

To appear in*East J. Approx.*

- and some related open problems
- Schmidt's inequality

*East J. Approx.***3**(1997), no. 2, 11-29. - $L_p$-error bounds for Hermite interpolation and the associated Wirtinger inequalities

*Constr. Approx.***13**(1997), no. 4, 461-479. - Symmetries of Linear Functionals

*Approximation Theory VIII - Vol. 1*, 541--550, (edited by C. K. Chui and L. L. Schumaker), World Scientific, 1995. - A multivariate form of Hardy's inequality and $L_p$-error bounds for multivariate Lagrange interpolation schemes

*SIAM J. Math. Anal.***28**(1997), no. 1, 233-258.**97h:41020** - Integral error formulae for the scale of mean value interpolations which includes Kergin and Hakopian interpolation

*Numer. Math.***77**(1997), no. 1, 105--122. - Dissertation (University of Wisconsin-Madison, May 1995)

- Error formulae for generalised Taylor interpolation
- Least rules and their numeric and symbolic calculation
- A homothety based argument for computing the best constant in some Hardy's inequalities for the complement of bounded domain
- The eigenstructure of the Bernstein operator

These html abstracts were created by the Auckland Mathematics Department's preprint submission form (which I wrote), and are kept in this directory. The department also maintains a list of those which have not yet appeared, and check me on MathSciNet.

Maintained by Shayne Waldron (waldron@math.auckland.ac.nz)

Last Modified: .