46 citations · 73 across the 17 of their papers we have counts for
17 papers
The horizontal Laplacian of a Riemannian submersion with totally geodesic fibers and an integrable horizontal distribution
Tatsuya Tate
The purpose of this note is to study spectral properties of the horizontal Laplacian of a Riemannian submersion with totally geodesic fibers and an integrable horizontal distributi…
An eigenfunction expansion formula for one-dimensional two-state quantum walks
Tatsuya Tate
The purpose of this paper is to give a direct proof of an eigenfunction expansion formula for one-dimensional 2-state quantum walks, which is an analog of that for Sturm-Liouville…
Eigenvalues of the Laplacian on the Goldberg-Coxeter constructions for - and -valent graphs
Toshiaki Omori, Hisashi Naito, Tatsuya Tate
We are concerned with spectral problems of the Goldberg-Coxeter construction for - and -valent finite graphs. The Goldberg-Coxeter constructions of a f…
Up and down grover walks on simplicial complexes
Xin Luo, Tatsuya Tate
A notion of up and down Grover walks on simplicial complexes are proposed and their properties are investigated. These are abstract Szegedy walks, which is a special kind of unitar…
Eigenvalues of quantum walks of Grover and Fourier types
Takashi Komatsu, Tatsuya Tate
A necessary and sufficient conditions for certain class of periodic unitary transition operators to have eigenvalues are given. Applying this, it is shown that Grover walks in any…
Eigenvalues, absolute continuity and localizations for periodic unitary transition operators
Tatsuya Tate
The localization phenomenon for periodic unitary transition operators on a Hilbert space consisting of square summable functions on an integer lattice with values in a complex vect…