1 citations · 1 across the 8 of their papers we have counts for
8 papers
A Leibniz rule of distributional pairing and hyperforce sum rule
Takashi Maruyama, Tatsuki Seto, Viktor Zaverkin +1
We reformulate and generalize the equilibrium hyperforce sum rule, a generalization of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy, by employing the Schwartz space an…
A Young-type integration on self-similar sets in intervals
Takashi Maruyama, Tatsuki Seto
We introduce a generalization of the Young integration on self-similar sets defined in a closed interval and give a sufficient condition of its integrability. We also prove integra…
A combinatorial integration on the Cantor dust
Takashi Maruyama, Tatsuki Seto
In this paper, we generalize the Cantor function to -dimensional cubes and construct a cyclic -cocycle on the Cantor dust. This cocycle is non-trivial on the pullback of the…
A combinatorial Fredholm module on self-similar sets built on -cubes
Takashi Maruyama, Tatsuki Seto
We construct a Fredholm module on self-similar sets such as the Cantor dust, the Sierpinski carpet and the Menger sponge. Our construction is a higher dimensional analogue of Conne…
A cyclic cocycle and relative index theorems on partitioned manifolds
Tatsuki Seto
In this paper, we extend Roe's cyclic -cocycle to relative settings. We also prove two relative index theorems for partitioned manifolds by using its cyclic cocycle, which are g…
A note on Atiyah's -index theorem in Heisenberg calculus
Tatsuki Seto
In this note, we prove an index theorem on Galois covering for Heisenberg elliptic differential operators, which is not elliptic, analogous to Atiyah's -index theorem. This note…
Toeplitz operators and the Roe-Higson type index theorem
Tatsuki Seto
Let be a complete Riemannian manifold and assume that is partitioned by a hypersurface . In this paper we introduce a novel class of functions on non…
Toeplitz operators and the Roe-Higson type index theorem in Riemannian surfaces
Tatsuki Seto
We study a two dimensional analogue of the Roe-Higson index theorem for a partitioned manifold. We prove that Connes' pairing of some invertible element with Roe's cyclic one-cocyc…