## Hyperholomorphic Function Theory and Clifford Analyticity.

We cordially invite the interested authors to contribute their original research papers as well as good expository papers to this special issue that will make better improvement on the theory of Clifford analysis and its application to mathematical physics, new approaches to differential geometry using Clifford’s geometric analysis. Potential topics include but are not limited to: Theory of hyperholomorphic functions, regular functions, monogenic functions, hypercomplex number, dual number systems, spilt number systems, bicomplex numbers, and split biquaternions and pseudoquaternions Analytic extensions and applicationsGeneral theory of complex analytic spacesComplex partial differential operators, quaternion matrix equations, and generalized Cauchy-Riemann systems Domains of hyperholomorphyComplex function spaces and hyperconjugate harmonic functionBroadly, recent advances on complex analysisBefore submission authors should carefully read over the journal’s Authors Guidelines, which are located at http://www.hindawi.com/journals/aaa/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/submit/journals/aaa/hyper/ according to the following timetable: Manuscript DueFriday, 15 November 2013First Round of ReviewsFriday, 7 February 2014Publication DateFriday, 4 April 2014

## Preprint “Special functions of hypercomplex variable on the lattice based on SU(1,1)”

Based on the representation of a set of canonical operators on the lattice , which are Clifford-vector-valued, we will introduce new families of special functions of hypercomplex variable possessing symmetries. The Fourier decomposition of the space of Clifford-vector-valued polynomials with respect to the – module gives rise to the construction of new families of polynomial sequences as eigenfunctions of a coupled system involving forward/backward discretizations of the Euler operator .

Moreover, the interpretation of the one-parameter representation of the Lie group as a semigroup will allows us to describe the polynomial solutions of a homogeneous Cauchy problem on involving the differencial-difference operator .

**arXiv preprint:** http://arxiv.org/abs/1304.7191v2

**Related arXiv preprints:**

*(Discrete) Almansi Type Decompositions: An umbral calculus framework based on symmetries*–http://arxiv.org/abs/1102.5434.*Fischer Decomposition for Difference Dirac Operators*–http://arxiv.org/abs/math/0609823.

**Related posts:**

## Discrete Clifford Analysis (2009-2013).

This thesis studies the fundamentals of a higher dimensional discrete function

theory using the Clifford Algebra setting. This approach combines the ideas of

Umbral Calculus and Differential Forms. Its powerful rests mostly on the

interplay between both languages. This allowed the construction of intertwining

operators between continuous and discrete structures, lifting the well known

results from continuum to discrete.

Furthermore, this resulted in a mimetic transcription of basis polynomial,

generating functions, Fischer Decomposition, Poincaré and dual-Poincaré

lemmata, Stokes theorem and Cauchy’s formula.

This theory also includes the description discrete counterparts of differential

forms, vector-fields and discrete integration. Indeed the resulted construction of

discrete differential forms, discrete vector-fields and discrete integration in

terms of barycentric coordinates leads to the correspondence between the

theory of Finite Differences and the theory of Finite Elements, which gives a

core of promising applications of this approach in numerical analysis. Some

preliminary ideas on this point of view were presented in this thesis.

We also developed some preliminary results in the theory of discrete

monogenic functions on simplicial complexes. Some connections with

Combinatorics and Quantum Mechanics were also presented along this thesis.

Abstract of my dissertation which provides me the doctor degree in mathematics (March 26, 2009). In a couple of weeks I wish to disseminate some new material with the goal to continue developing the discrete Clifford analysis arena.

The dissemation of new material likewise some ongoing research around was the main motivation to create this blog. In a nearly future, I wish to create a research networking project within this topic with the goal to promote research discussions around this topic. If you are still interested in join in, please feel it free to send me an e-mail.

## ICCA10 @Tartu

The 10th International Conference on Clifford Algebras and Their Applications in Mathematical Physics (ICCA10) will be held in Tartu, Estonia from August 4 till August 9, 2014.

Information concerning the Local Organinzing Committe, International Advisory Board, aims and scope of ICCA10 on the webpage http://icca10.ut.ee/. Registration will be possible around mid August 2013.

## ICNAAM 2013.

On behalf of Professors Klaus Guerlebeck and Wolfgang Sproessig, I would like to invite you to participate in ICNAAM 2013. The conference will take place from **September 21 – 27, 2013**, at the **Rodos Palace Hotel, Rhodes, Greece**.Below you will find the link for the pdf-file with the announcement and some necessary information. General information on the complete ICNAAM conference you can find on *http://www.icnaam.org/.*

**Invitation Letter:** 13-Rhodes

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## Call for papers for 100th Volume – Vacuum

The journal

Vacuumis approaching a new landmark. Having started publication in 1952, we will publishVacuum’s100th volume this autumn. An event we want to mark by making this a special volume.Volume 100 will be an open access volume, freely available to everyone, and providing the papers with maximum exposure. Long-time Editor, Prof. John Colligon, has agreed to write an article on the history of the journal.

In addition, we would like to invite you to contribute a

Rapid Communicationto Volume 100.Vacuumhas recently introduced a Rapid Communication section for short papers that will be reviewed promptly. The articles have to fit theguidelinesand contain new data worthy of rapid communication.Rapid Communication contributions that we receive before

June 15, 2013will be considered for Volume 100. Please join us in celebrating! Submit your best work and receive maximum exposure! We look forward to receiving your manuscripts.