Ebook: Wavelets, Multiscale Systems and Hypercomplex Analysis
Author: Ricardo Abreu-Blaya Juan Bory-Reyes (auth.) Daniel Alpay Annemarie Luger Harald Woracek (eds.)
- Tags: Operator Theory, Systems Theory Control, Functions of a Complex Variable, Analysis, Abstract Harmonic Analysis
- Series: Operator Theory: Advances and Applications 167
- Year: 2006
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
From a mathematical point of view it is fascinating to realize that most, if not all, of the notions arising from the theory of analytic functions in the open unit disk have counterparts when one replaces the integers by the nodes of a homogeneous tree. It is also fascinating to realize that a whole function theory, different from the classical theory of several complex variables, can be developped when one considers hypercomplex (Clifford) variables, Fueter polynomials and the Cauchy-Kovalevskaya product, in place of the classical polynomials in three independent variables.
This volume contains a selection of papers on the topics of Clifford analysis and wavelets and multiscale analysis, the latter being understood in a very wide sense. The theory of wavelets is mathematically rich and has many practical applications.
Contributors: R. Abreu-Blaya, J. Bory-Reyes, F. Brackx, Sh. Chandrasekaran, N. de Schepper, P. Dewilde, D.E. Dutkay, K. Gustafson, H. Heyer, P.E.T. Jorgensen, T. Moreno-García, L. Peng, F. Sommen, M.W. Wong, J. Zhao, H. Zhu
From a mathematical point of view it is fascinating to realize that most, if not all, of the notions arising from the theory of analytic functions in the open unit disk have counterparts when one replaces the integers by the nodes of a homogeneous tree. It is also fascinating to realize that a whole function theory, different from the classical theory of several complex variables, can be developped when one considers hypercomplex (Clifford) variables, Fueter polynomials and the Cauchy-Kovalevskaya product, in place of the classical polynomials in three independent variables.
This volume contains a selection of papers on the topics of Clifford analysis and wavelets and multiscale analysis, the latter being understood in a very wide sense. The theory of wavelets is mathematically rich and has many practical applications.
Contributors: R. Abreu-Blaya, J. Bory-Reyes, F. Brackx, Sh. Chandrasekaran, N. de Schepper, P. Dewilde, D.E. Dutkay, K. Gustafson, H. Heyer, P.E.T. Jorgensen, T. Moreno-Garc?a, L. Peng, F. Sommen, M.W. Wong, J. Zhao, H. Zhu
From a mathematical point of view it is fascinating to realize that most, if not all, of the notions arising from the theory of analytic functions in the open unit disk have counterparts when one replaces the integers by the nodes of a homogeneous tree. It is also fascinating to realize that a whole function theory, different from the classical theory of several complex variables, can be developped when one considers hypercomplex (Clifford) variables, Fueter polynomials and the Cauchy-Kovalevskaya product, in place of the classical polynomials in three independent variables.
This volume contains a selection of papers on the topics of Clifford analysis and wavelets and multiscale analysis, the latter being understood in a very wide sense. The theory of wavelets is mathematically rich and has many practical applications.
Contributors: R. Abreu-Blaya, J. Bory-Reyes, F. Brackx, Sh. Chandrasekaran, N. de Schepper, P. Dewilde, D.E. Dutkay, K. Gustafson, H. Heyer, P.E.T. Jorgensen, T. Moreno-Garc?a, L. Peng, F. Sommen, M.W. Wong, J. Zhao, H. Zhu
Content:
Front Matter....Pages i-xi
Teodorescu Transform Decomposition of Multivector Fields on Fractal Hypersurfaces....Pages 1-16
Metric Dependent Clifford Analysis with Applications to Wavelet Analysis....Pages 17-67
A Hierarchical Semi-separable Moore-Penrose Equation Solver....Pages 69-85
Methods from Multiscale Theory and Wavelets Applied to Nonlinear Dynamics....Pages 87-126
Noncommutative Trigonometry....Pages 127-155
Stationary Random Fields over Graphs and Related Structures....Pages 157-171
Matrix Representations and Numerical Computations of Wavelet Multipliers....Pages 173-182
Clifford Algebra-valued Admissible Wavelets Associated to More than 2-dimensional Euclidean Group with Dilations....Pages 183-190
From a mathematical point of view it is fascinating to realize that most, if not all, of the notions arising from the theory of analytic functions in the open unit disk have counterparts when one replaces the integers by the nodes of a homogeneous tree. It is also fascinating to realize that a whole function theory, different from the classical theory of several complex variables, can be developped when one considers hypercomplex (Clifford) variables, Fueter polynomials and the Cauchy-Kovalevskaya product, in place of the classical polynomials in three independent variables.
This volume contains a selection of papers on the topics of Clifford analysis and wavelets and multiscale analysis, the latter being understood in a very wide sense. The theory of wavelets is mathematically rich and has many practical applications.
Contributors: R. Abreu-Blaya, J. Bory-Reyes, F. Brackx, Sh. Chandrasekaran, N. de Schepper, P. Dewilde, D.E. Dutkay, K. Gustafson, H. Heyer, P.E.T. Jorgensen, T. Moreno-Garc?a, L. Peng, F. Sommen, M.W. Wong, J. Zhao, H. Zhu
Content:
Front Matter....Pages i-xi
Teodorescu Transform Decomposition of Multivector Fields on Fractal Hypersurfaces....Pages 1-16
Metric Dependent Clifford Analysis with Applications to Wavelet Analysis....Pages 17-67
A Hierarchical Semi-separable Moore-Penrose Equation Solver....Pages 69-85
Methods from Multiscale Theory and Wavelets Applied to Nonlinear Dynamics....Pages 87-126
Noncommutative Trigonometry....Pages 127-155
Stationary Random Fields over Graphs and Related Structures....Pages 157-171
Matrix Representations and Numerical Computations of Wavelet Multipliers....Pages 173-182
Clifford Algebra-valued Admissible Wavelets Associated to More than 2-dimensional Euclidean Group with Dilations....Pages 183-190
....