M. Suga, H. Miura, H. Fujiwara, T. Yamamoto, T. Tanaka, Q. YU, K. Arai, J. P. GONG, G. Nakamura, H. Ikehira, and T. Obata Graduate School of Technology, Chiba University, Chiba, Chiba, Japan, Molecular Imaging Center, National Institute of Radiological Sciences, Chiba, Chiba, Japan, Graduate School of Informatics, Kyoto University, Faculty of Engineering, Gunma University, Graduate School of Sc...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

The standard Lichnerowicz comparison theorem states that if the Ricci curvature of a closed, Riemannian n-manifold M satisfies Ric (X,X) ≥ a (n − 1) |X| for every X ∈ TM for some fixed a > 0, then the smallest positive eigenvalue λ of the Laplacian satisfies λ ≥ an. The Obata theorem states that equality occurs if and only if M is isometric to the standard n-sphere of constant sectional curvatu...

In a complete Riemannian manifold (M,g) if the hessian of a real valued function satisfies some suitable conditions then it restricts the geometry of (M,g). In this paper we characterize all compact rank-1 symmetric spaces, as those Riemannian manifolds (M,g) admitting a real valued function u such that the hessian of u has atmost two eigenvalues −u and − 2 , under some mild hypothesis on (M,g)...

in this paper, we determine the structure of the space of multipliers of the range of a composition operator cφ that induces by the conditional expectation between two lp() spaces.

D. Yamamoto, A. Tandoc, III, E. Mercado, F. Quicho, S. Lupisan, M. Obata-Saito, M. Okamoto, A. Suzuki, R. Tamaki, L. Sombrero, R. Olveda and H. Oshitani 1) Tohoku-RITM Collaborating Research Center for Emerging and Reemerging Infectious Diseases, Metro Manila, Philippines, 2) Department of Virology, Tohoku University Graduate School of Medicine, Sendai, Japan, 3) Research Institute for Tropical...