Coherent Combination of Baryon Acoustic Oscillation Statistics and Peculiar Velocity Measurements from Redshift Survey

New statistical method is proposed to coherently combine Baryon Acoustic Oscillation statistics (BAO) and peculiar velocity measurements exploiting decomposed density--density and velocity--velocity spectra in real space from the observed redshift distortions in redshift space, 1) to achieve stronger dark energy constraints, sigma(w)=0.06 and sigma(w_a)=0.20, which are enhanced from BAO or velocity measurements alone, and 2) to cross--check consistency of dark energy constraints from two different approaches; BAO as geometrical measurements and peculiar velocity as large scale structure formation observables.