Guillem CobosInstitute of Technology, Tralee · Department of Computing
Guillem Cobos
Master of Science
About
3
Publications
113
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5
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Citations since 2017
Introduction
My research is on the ultra hyperbolic equation in 4 variables. I am exploiting its invariance under conformal mappings of the pseudo-Euclidean space R(2,2). I have so far found new mean value theorems for solutions of the ultrahyperbolic equation, which extend those known from Asgeirsson's theorem.
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Publications
Publications (3)
Asgeirsson's theorem establishes a mean value property for solutions of the ultrahyperbolic equation. In the case of four variables, it states that the integrals of a solution over certain pairs of conjugate circles are the same. In this paper, the invariance of the four dimensional ultrahyperbolic equation under conformal maps of the pseudo-Euclid...
In 1937 Asgeirsson established a mean value property for solutions of the general ultra-hyperbolic equation in $2n$ variables. In the case of four variables, it states that the integrals of a solution over certain pairs of conjugate circles are the same. In this paper we extend this result to non-degenerate conjugate conics, which include the origi...
In 1937 Asgeirsson established a mean value property for solutions of the general ultra-hyperbolic equation in $2n$ variables. In the case of four variables, it states that the integrals of a solution over certain pairs of conjugate circles are the same. In this paper we extend this result to non-degenerate conjugate conics, which include the origi...
Projects
Project (1)
My research is on the ultra hyperbolic equation in 4 variables. I am exploiting its invariance under conformal mappings of the pseudo-Euclidean space R(2,2). In this way, I have so far found new mean value theorems for solutions of the ultrahyperbolic equation, which extend those from Asgeirsson's theorem. The plan is to keep doing so (there are further integral theorems on degenerate curves which need to be found), and apply it to solve the characteristic boundary value problem.
