L^2(R^2,H;dx)上以实值内积定义的连续小波变换

Continuous wavelet transform on the space L^2(R^2,H;dx) by defining real valued inner product

目的建立平方可积的四元数函数空间L2(R2,H;dx)上的连续小波变换的Parseval等式及反方程。方法定义四元数集合的实值内积,将空间L2(R2,H;dx)分解成为不可约不变子空间的直和,给出容许条件的特征。结果建立了四元数值函数空间小波变换的Parseval等式。结论在弱的意义下给出了小波变换的反方程。

Aim To establish the Parseval＇s formula and reconstruction formula for the continuous wavelet transform on the space L^2 （R^2 , H;dx）. Methods By using real valued inner product on H, L^2 （R^2 ,H;dx） was decomposed into the direct sum of the irreducible invariant subspaces and the characterization of the admissibility condition was given. Results This paper establish the Parseval＇s formula for the continuous wavelet transform on L2 （R^2 ,H;dx）. Conclusion The inverse wavelet transform in the weak sense was get.