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MRA Parseval frame wavelets and their multipliers in \(L^2(\mathbb R^n)\). (English) Zbl 1183.93124
Summary: We characterize all generalized lowpass filters and MultiResolution Analysis (MRA) Parseval frame wavelets in \(L^2(\mathbb R^n)\) with matrix dilations of the form \((Df)(x)=2f(Ax)\), where A is an arbitrary expanding \(n\times n\) matrix with integer coefficients, such that \(|\det A|=2\). At first, we study the pseudo-scaling functions, generalized lowpass filters, and MRA Parseval frame wavelets and give some important characterizations about them. Then, we describe the multiplier classes associated with Parseval frame wavelets in \(L^2(\mathbb R^n)\) and give an example to prove our theory.

MSC:
93E11 Filtering in stochastic control theory
65T60 Numerical methods for wavelets
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