Holon Institute of Technology
 
Dear Colleagues,
 
Our next Colloquium in Mathematics and Computer Science will take
place on Tuesday, March 19, at 12:00.
 
Speaker: Dr. Daniel Alayon-Solarz
 
Affiliation: Departamento de Matematicas, Universidad Simón Bolívar
in Caracas, Venezuela
 
Title:  On Operators associated to the Cauchy-Riemann operator in
elliptic complex numbers
 
Date: Tuesday, March 19, 2013
 
Time: 12:00
 
Venue: Room 424/8, Science Building
 
Abstract:
 
The Cauchy-Kovaleskaya Theorem provides sufficient conditions for an
elliptic linear equation on the plane with evolution in time to have
solutions with prescribed initial value functions. That these
conditions cannot be freely relaxed comes by the celebrated Lewy's
example of a system with no solutions. In [3] the technique of
associated operators is used to establish conditions for solvability
provided the initial pair is holomorphic. This result is further
generalized to the case when the initial pair is holomorphic in
elliptic complex numbers in [1]. In this talk we will discuss some
key aspects of this latter result and how can these be used as a tool
to generalize results valid for ordinary holomorphic functions.
 
[1] Alayon-Solarz D., Vanegas C.J., "Operators Associated to the
Cauchy-Riemann Operator in Elliptic Complex Numbers" Advances in
Applied Clifford Algebras, DOI: 10.1007/s00006-011-0306-4, 2011.
 
[2] Lewy, H., "An example of a smooth linear partial differential
equation without solution", Annals of Mathematics 66 (1): 155-158,
doi:10.2307/1970121,1957.
 
[3] Son L. H. and Tutschke W., "First Order differential operators
associated to the Cauchy-Riemann equations in the plane", Complex
Variables and Elliptic Equations, Vol. 48, No. 9, pp 797-801, 2003.
 
This is a joint work with C.J. Vanegas.
 
Light refreshments will be served at 11:45 am. Everybody is welcome.
 
Looking forward to seeing you all,
 
                 Anatoly Golberg, Dmitry Goldstein, Eugen Mandrescu
 
Holon Institute of Technology, 52 Golomb St, Holon, 03-5026560,
 <http://www.hit.ac.il/acc/golberga/Events/Colloquia.html>
 
---------------------------------------------------------
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Anatoly Golberg   <golberga@hit.ac.il>