TY - BOOK

T1 - Wavelets, Multiscale Systems and Hypercomplex Analysis

AU - Alpay, Daniel

A2 - Luger, Annemarie

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Clifford analysis

KW - Complex analysis

KW - Hypercomplex analysis

KW - Nonlinear dynamics

KW - Operator theory

KW - Random field

KW - System theory

KW - Teodorescu transform

KW - Wavelets

KW - analysis

U2 - https://doi.org/10.1007/3-7643-7588-4

DO - https://doi.org/10.1007/3-7643-7588-4

M3 - Book

SN - 9783764375881

T3 - Operator Theory: Advances and Applications

BT - Wavelets, Multiscale Systems and Hypercomplex Analysis

PB - Birkhäuser Verlag

CY - Basel Switzerland; Boston

ER -