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Regularization Of Inverse Problems

Recently Appell systems of monogenic polynomials in ℝ3 were constructed by several authors Main purpose of this paper is the description of another Appell system that is complete in the space of square integrable quaternion-valued functions A new Taylor-type series expansion based on the Appell polynomials is presented, which can be related to the corresponding Fourier series analogously as in the complex one-dimensional case These results find applications in the description of the hypercomplex derivative, the monogenic primitive of a monogenic function and the characterization of functions from the monogenic Dirichlet space Copyright © 2009 John Wiley & Sons, Ltd

On a generalized Appell system and monogenic power series

State of the art of corner point singularities under in-plane and out-of-plane loading

http://repositorium.sdum.uminho.pt/bitstream/1822/14436/1/CacaoFalcaoMalonek2011.pdf

Laguerre derivative and monogenic Laguerre polynomials: An operational approach

Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as sl(2,C)-modules. As finite-dimensional irreducible sl(2,C)-modules, they have canonical bases which are, by construction, orthogonal. In this note, we show that these orthogonal bases form the Appell system and coincide with those constructed recently by S. Bock and K. Guerlebeck. Moreover, we obtain simple expressions of elements of these bases in terms of the Legendre polynomials.

Canonical bases for sl(2,C)-modules of spherical monogenics in dimension 3

The main objective of this article is to consider complete orthonormal systems of monogenic polynomials together with their hypercomplex derivatives. Desired is that the derivatives of the basis polynomials are again basis functions from the original system. Based on this result, we prove an orthogonal decomposition of the space of square integrable monogenic functions with respect to the derivatives of arbitrary order. §Dedicated to Professor Guochun Wen on the occasion of his 75th birthday.

On derivatives of spherical monogenics

The main goal of this paper is to construct a spatial analog to the Kolosov–Muskhelishvili formulae using the framework of the hypercomplex function theory. We prove a generalization of Goursat's representation theorem for solutions of the biharmonic equation in three dimensions. On the basis of this result, we construct explicitly hypercomplex displacement and stress formulae in terms of two monogenic functions. Copyright © 2008 John Wiley & Sons, Ltd.

On a spatial generalization of the Kolosov-Muskhelishvili formulae

The main aim of this paper is to recall the notion of the Gelfand-Tsetlin bases (GT bases for short) and to use it for an explicit construction of orthogonal bases for the spaces of spherical monogenics (i.e., homogeneous solutions of the Dirac or the generalized Cauchy-Riemann equation, respectively) in dimension 3. In the paper, using the GT construction, we obtain explicit orthogonal bases for spherical monogenics in dimension 3 having the Appell property and we compare them with those constructed by the rst and the second author recently (by a direct analytic approach).

/pdf/gelfand-tsetlin-bases-for-spherical-monogenics-in-dimension-g3tv5lzxvj.pdf

Gelfand–Tsetlin bases for spherical monogenics in dimension 3

https://hal.archives-ouvertes.fr/hal-01275173/document

S. Bock

Papers

On a generalized Appell system and monogenic power series

On derivatives of spherical monogenics

On a spatial generalization of the Kolosov-Muskhelishvili formulae

Gelfand–Tsetlin bases for spherical monogenics in dimension 3

Three-dimensional elasticity based on quaternion-valued potentials