## Wavelet Analysis and Multiresolution MethodsThis volume contains papers selected from the Wavelet Analysis and Multiresolution Methods Session of the AMS meeting held at the University of Illinois at Urbana-Champaign. The contributions cover: construction, analysis, computation and application of multiwavelets; scaling vectors; nonhomogenous refinement; mulivariate orthogonal and biorthogonal wavelets; and other related topics. |

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### Contents

Higher Order Multivariate Wavelet Type Approximation | 1 |

Nonlinear Haar Approximation of Functions with Bounded Mixed Derivative | 21 |

Wavelet Coefficients Associated with Translation and Rotation Transform | 43 |

Multiwavelet Construction via the Lifting Scheme | 51 |

Methods in Nonhomogeneous Refinement | 75 |

Construction of Multivariate Biorthogonal Wavelets by CBC Algorithm | 97 |

Construction of Prewavelets with Minimum Support over Triangulations | 137 |

Applications in Industry | 159 |

Multiwavelet Solutions for the Dirichlet Problem | 233 |

Calculating the Spectral Radius of a Set of Matrices | 247 |

Polynomial Frames for the Detection of Singularities | 265 |

Sampling Bounds and Stability | 291 |

On the Construction of Positive Scaling Vectors | 292 |

A Geometric Approach to Ergodic NonHomogeneous Markov Chains | 299 |

Conversion between Orthogonal and Biorthogonal Wavelets | 325 |

Index | 337 |

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Algebra analysis apparatus Applications approximation associated assume bases basis biorthogonal wavelets bounded called CBC algorithm classes coefficients compact compactly supported components compute condition consider constant construction continuous convergence corresponding Daubechies defined definition denote depend derivative Differential discuss dual equation ergodic estimates example exists Figure filter finite formula Fourier frame given gives Haar Hence implies inequality integer interval introduced Lemma lifting linear Markov mask Math Mathematics matrix method multiwavelets norm Note obtain operator optimal orthogonal pair particular polynomials positive prewavelets processing Proof properties Proposition proved provides References refinable function respectively result sampling satisfies scaling function scaling vector sequence signal similar simple smoothness solution space spectral radius stability step sum rules Suppose symmetric Theorem Theory tion transform unique University values vertices wavelet transform