109 citations · 252 across the 20 of their papers we have counts for
20 papers
Riesz Energy, Discrepancy, and Optimal Transport of Determinantal Point Processes on the Sphere and the Flat Torus
Bence Borda, Peter Grabner, Ryan W. Matzke
Determinantal point processes exhibit an inherent repulsive behavior, thus providing examples of very evenly distributed point sets on manifolds. In this paper, we study the so-cal…
Needlets Liberated
Johann S. Brauchart, Peter J. Grabner, Ian H. Sloan +1
Spherical needlets were introduced by Narcowich, Petrushev, and Ward to provide a multiresolution sequence of polynomial approximations to functions on the sphere. The needlet cons…
Riesz and Green energy on projective spaces
Austin Anderson, Maria Dostert, Peter J. Grabner +2
In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projec…
How well-conditioned can the eigenvalue problem be?
Carlos Beltrán, Laurent Bétermin, Peter Grabner +1
The condition number for eigenvalue computations is a well--studied quantity. But how small can we expect it to be? Namely, which is a perfectly conditioned matrix w.r.t. eigenvalu…
Asymptotic expansions for the coefficients of extremal quasimodular forms and a conjecture of Kaneko and Koike
Peter J. Grabner
Extremal quasimodular forms have been introduced by M.~Kaneko and M.Koike as as quasimodular forms which have maximal possible order of vanishing at . We show an asymptoti…
Quasimodular forms as solutions of Modular differential equations
Peter J. Grabner
We study quasimodular forms of depth and determine under which conditions they occur as solutions of modular differential equations. Furthermore, we study which modular dif…