arXiv subjects
Publications and source records attributed to Michio Seto.
It is known that invariant subspaces of classical Jordan blocks of the Hardy space over the open unit disc are described by factorizations of inner functions. In the polydisc setting, Jordan blocks are tensor products of one-variable Jordan blocks. We provide representations of their doubly commuting invariant subspaces.
We study de Branges--Rovnyak spaces parametrized by L\"{o}wner equations. A new approach based on the L\"{o}wner theory to problem ``Find concrete elements in de Branges--Rovnyak spaces'' is given.
In this paper, we focus on an indefinite structure lying behind the Bergman kernel on the open unit disk. In particular, an invariant distance, birational maps and an indefinite kernel are constructed from the Bergman kernel, and we deal with their interaction.
This paper addresses distributed learning of a complex object for multiple networked robots based on distributed optimization and kernel-based support vector machine. In order to overcome a fundamental limitation of polynomial kernels assumed in our antecessor, we employ Gaussian kernel as a kernel function for classification. The Gaussian kernel prohibits the robots to share the function through a finite number of equality constraints due to its infinite dimensionality of the function space. We thus reformulate the optimization problem assuming that the target function space is identified with the space spanned by the bases associated with not the data but a finite number of grid points. The above relaxation is shown to allow the robots to share the function by a finite number of equality constraints. We finally demonstrate the present approach through numerical simulations.
In this paper, we give a new approach to the theory of strictly positive kernels. Our method is based on the structure of Fock spaces. As its applications, various examples of strictly positive kernels are given. Moreover, we give a new proof of the universal approximation theorem for the Gauss kernel.
In this note, we give a new property of de Branges-Rovnyak kernels. As the main theorem, it is shown that the exponential of de Branges-Rovnyak kernel is strictly positive definite if the inner part of the corresponding Schur class function is nontrivial.
Indefinite Schwarz-Pick inequalities for holomorphic self-maps of the bidisk are given as application of the spectral theory on Hilbert modules.
We study triplets of Hilbert space operators satisfying a certain inequality. A range inclusion theorem with norm estimate for those triplets is given with the language of Kre\u{\i}n space geometry and de Branges-Rovnyak space theory.
In this paper, we introduce the notion of reproducing kernel Hilbert spaces for graphs and the Gram matrices associated with them. Our aim is to investigate the Gram matrices of reproducing kernel Hilbert spaces. We provide several bounds on the entries of the Gram matrices of reproducing kernel Hilbert spaces and characterize the graphs which attain our bounds.