Analyticity of solutions to a quadratic system of Schrödinger equations without mass resonance condition

We consider the Cauchy problem for a quadratic system of Schrödinger equations in space dimensions n≥4 without mass resonance condition. Analytic smoothing effect for the quadratic system of Schrödinger equations under the mass resonance condition for data which satisfy exponentially decaying condition has been studied in [14]. In this study, we construct global solutions in the analytic Hardy space via the phase modulation operator, based on the scale critical Sobolev space H˙n/2−2 with data like the test functions of Fourier hyperfunctions, under the condition m1≤m2≤(1+4/n)m1 between two masses m1 and m2.