  Thermodynamic and dynamical properties of filling-control metal-insulator
transition (MIT) in the Hubbard model are studied by the operator projection
method, especially in two dimensions. This is a non-perturbative analytic
approach to many-body systems. The present theory incorporates the
Mott-Hubbard, Brinkman-Rice and Slater pictures of the MIT into a unified
framework, together with reproducing low-energy narrow band arising from
spin-charge fluctuations. At half filling, single-particle spectra $A(\omega,
k)$ show formation of two Hubbard bands and their antiferromagnetic shadows
separated by a Mott gap in the plane of energy $\omega$ and momentum $k$ with
lowering temperatures. These four bands produce splitting to two low-energy
narrow bands and two SDW-like bands in the dispersion. Near half filling, the
low-energy narrow band persists at low temperatures. This narrow band has a
particularly weak dispersion and large weights around $(\pi, 0)$ and $(0, \pi)$
momenta. The velocity of these low-energy excitations is shown to vanish
towards the MIT, indicating the mass divergence as in the Brinkman-Rice
picture, but most prominently around $(\pi,0)$ and $(0,\pi)$ with strong
momentum dependence. This reflects the suppression of the coherence near the
MIT. Main structures in $A(\omega, k)$ show remarkable similarities to quantum
Monte-Carlo results in two dimensions as well as in the one-dimensional Hubbard
model. The charge compressibility appears to diverge with decreasing doping
concentration in both one and two dimensions in agreement with the exact and
quantum Monte-Carlo results. We also discuss implications of the flat
dispersion formed near the Fermi level to the observations in high-$\Tc$
cuprate superconductors.
