6 papers · 1 filter
Quantizing Delsarte Theory
Ryutaro Misawa
We develop Delsarte theory for quantum association schemes, allowing both composition and the quantum Schur product to be noncommutative. A MacWilliams identity and positivity of t…
Spherical Designs with Infinite Harmonic Strength
Ryutaro Misawa, Yusaku Nishimura
In this paper, we study the existence problem for spherical \(T\)-designs on the \(d\)-dimensional sphere, where \(T\) is an infinite subset of \(\mathbb N\). We show that, if \(d\…
Explicit construction of spherical - and -designs
Ryutaro Misawa
This paper develops an explicit and implementable framework for constructing spherical designs by lifting point sets from tight fusion frames. By combining existing ingredients, we…
Constructing spherical designs using tight -fusion frames
Ryutaro Misawa
In this paper, we study conditions under which a finite subset of the unit sphere becomes a spherical -design, when is constructed by the…
Spherical Designs on of Finite Harmonic Strength
Ryutaro Misawa, Yusaku Nishimura
We study exact harmonic strengths of finite spherical designs on the unit circle. For a nonempty finite set \(X\subset S^1\), let \(\Hst(X)\) be the set of positive integers \(k\)…
Antipodality of spherical designs with odd harmonic indices
Ryutaro Misawa, Akihiro Munemasa, Masanori Sawa
We determine the smallest size of a non-antipodal spherical design with harmonic indices to be , where is a positive integer. This is achieved by pro…