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>