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pro vyhledávání: '"Tate, Tatsuya"'
Autor:
Tate, Tatsuya
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 operators due to Weyl, Stone, Titchmarsh and Kodaira. In the context o
Externí odkaz:
http://arxiv.org/abs/2109.09942
Publikováno v:
The Electronic Journal of Combinatorics, 26(3) (2019), #P3.7
We are concerned with spectral problems of the Goldberg-Coxeter construction for $3$- and $4$-valent finite graphs. The Goldberg-Coxeter constructions $\mathrm{GC}_{k,l}(X)$ of a finite $3$- or $4$-valent graph $X$ are considered as "subdivisions" of
Externí odkaz:
http://arxiv.org/abs/1807.10891
Autor:
Luo, Xin, Tate, Tatsuya
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 unitary operators on a Hilbert space. The operators introduced in the presen
Externí odkaz:
http://arxiv.org/abs/1706.09682
Autor:
Komatsu, Takashi, Tate, Tatsuya
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 dimension has both of $\pm 1$ as eigenvalues and it has no other eigen
Externí odkaz:
http://arxiv.org/abs/1704.05236
Autor:
Tate, Tatsuya
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 vector space, which is a generalization of the discrete-time quantum walks
Externí odkaz:
http://arxiv.org/abs/1411.4215
Autor:
Tate, Tatsuya
Publikováno v:
Interdisciplinary Information Sciences 19, No. 2 (2013), 149--156
An explicit formula of the Hamiltonians generating one-dimensional discrete-time quantum walks is given. The formula is deduced by using the algebraic structure introduced previously. The square of the Hamiltonian turns out to be an operator without,
Externí odkaz:
http://arxiv.org/abs/1306.3557
Autor:
Tate, Tatsuya
Publikováno v:
Infin. Dimens. Anal. Quantum Probab. Relat. Top. Vol. 16, No. 2 (2013)
An algebraic structure for one-dimensional quantum walks is introduced. This structure characterizes, in some sense, one-dimensional quantum walks. A natural computation using this algebraic structure leads us to obtain an effective formula for the c
Externí odkaz:
http://arxiv.org/abs/1210.0631
Autor:
Sunada, Toshikazu, Tate, Tatsuya
Publikováno v:
Journal of Functional Analysis 262 (2012), 2608--2645
This paper gives various asymptotic formulae for the transition probability associated with discrete time quantum walks on the real line. The formulae depend heavily on the `normalized' position of the walk. When the position is in the support of the
Externí odkaz:
http://arxiv.org/abs/1108.1878
Autor:
Tate, Tatsuya
Publikováno v:
Journal of Functional Analysis 260 (2011), no. 2, 501-540
An asymptotic expansion formula of Riemann sums over lattice polytopes is given. The formula is an asymptotic form of the local Euler-Maclaurin formula due to Berline-Vergne. The proof given here for Delzant lattice polytopes is independent of the lo
Externí odkaz:
http://arxiv.org/abs/0908.3073
Autor:
Tate, Tatsuya
Publikováno v:
Contemporary Mathematics 484 (2007) 295-319
We define the notion of Bernstein measures and Bernstein approximations over general convex polytopes. This generalizes well-known Bernstein polynomials which are used to prove the Weierstrass approximation theorem on one dimensional intervals. We di
Externí odkaz:
http://arxiv.org/abs/0805.3379