Wavelets, Multiscale Systems and Hypercomplex Analysis by Ricardo Abreu-Blaya, Juan Bory-Reyes (auth.), Daniel Alpay,

By Ricardo Abreu-Blaya, Juan Bory-Reyes (auth.), Daniel Alpay, Annemarie Luger, Harald Woracek (eds.)

From a mathematical viewpoint it really is interesting to gain that almost all, if now not all, of the notions bobbing up from the speculation of analytic services within the open unit disk have opposite numbers whilst one replaces the integers through the nodes of a homogeneous tree. it's also attention-grabbing to achieve entire functionality idea, diverse from the classical concept of a number of complicated variables, will be developped whilst one considers hypercomplex (Clifford) variables, Fueter polynomials and the Cauchy-Kovalevskaya product, instead of the classical polynomials in 3 self sustaining variables.

This quantity includes a collection of papers at the issues of Clifford research and wavelets and multiscale research, the latter being understood in a really huge experience. the idea of wavelets is mathematically wealthy and has many sensible applications.

Contributors: R. Abreu-Blaya, J. Bory-Reyes, F. Brackx, Sh. Chandrasekaran, N. de Schepper, P. Dewilde, D.E. Dutkay, okay. Gustafson, H. Heyer, P.E.T. Jorgensen, T. Moreno-García, L. Peng, F. Sommen, M.W. Wong, J. Zhao, H. Zhu

Show description

Read Online or Download Wavelets, Multiscale Systems and Hypercomplex Analysis PDF

Best analysis books

Blow-up in Nonlinear Sobolev Type Equations (De Gruyter Series in Nonlinear Analysis and Applications)

The monograph is dedicated to the examine of initial-boundary-value difficulties for multi-dimensional Sobolev-type equations over bounded domain names. The authors reflect on either particular initial-boundary-value difficulties and summary Cauchy difficulties for first-order (in the time variable) differential equations with nonlinear operator coefficients with recognize to spatial variables.

The Future of the Telecommunications Industry: Forecasting and Demand Analysis

The purpose of this booklet, way forward for the Telecommunications undefined: Forecasting and insist research, is to explain prime study within the sector of empirical telecommunications call for research and forecasting within the mild of large marketplace and regulatory alterations. Its function is to teach the reader approximately how conventional analytic options can be utilized to evaluate new telecommunications items and the way new analytic innovations can greater deal with latest items.

Additional resources for Wavelets, Multiscale Systems and Hypercomplex Analysis

Sample text

M fixed, we then call Ckm = λ ∈ Cm : λ = λA ei1 ∧ ei2 ∧ · · · ∧ eik , A = (i1 , i2 , . . , the space spanned by the outer products of k different basis vectors. Note that the 0-vectors and 1-vectors are simply the scalars and Clifford-vectors; the 2-vectors are also called bivectors. 30 F. Brackx, N. De Schepper and F. 3. Embeddings of Rm By identifying the point (x1 , . . , xm ) ∈ Rm with the 1-vector x given by x = xj ej , the space Rm is embedded in the Clifford algebra Cm as the subspace of 1vectors R1m of the real Clifford algebra Rm .

Brackx, N. De Schepper and F. 3. 21. With respect to the orthonormal frame η j (j = 1, . . , m), the Dirac operator takes the form ∂x = ∂x j η j . j Proof. For the sake of clarity, we do not use the Einstein summation convention. We have consecutively ∂xj ej = ∂x = j j,k ⎛ ⎝ = t ∂xj g jk ek = ∂xj g jk Et ATtk j,k,t ⎞ ATtk g jk ∂xj ⎠ Et . 3) this becomes ∂x = t 1 ∂X t Et = λt ∂x t η t . 22. (i) A Cm -valued function F (x1 , . . , xm ) is called left monogenic in an open region of Rm if in that region ∂x [F ] = 0.

Then we consider the Clifford algebra-valued inner product f, g h(x) f † (x) g(x) dxM = Rm where dxM stands for the Lebesgue measure on Rm ; the associated norm then reads f 2 = [ f, f ]0 . The unitary right Clifford-module of Clifford algebra-valued measurable functions on Rm for which f 2 < ∞ is a right Hilbert-Clifford-module which we denote by L2 (Rm , h(x) dxM ). 46 F. Brackx, N. De Schepper and F. Sommen In particular, taking h(x) ≡ 1, we obtain the right Hilbert-module of square integrable functions: L2 Rm , dxM = f : Lebesgue measurable in Rm for which 1/2 f 2 = Rm |f (x)|20 dxM <∞ .

Download PDF sample

Rated 5.00 of 5 – based on 49 votes