Mathematical Proceedings of the Royal Irish Academy, Vol. 106A, No. 1 (JUNE 2006), pp. 97-113 (17 pages) We prove that two domains of holomorphy U and V in separable Fréchet spaces with the bounded ...

Elliptic equations play a central role in the study of steady-state phenomena across physics, engineering and geometry. Their analysis not only provides insights into the qualitative behaviour of ...

The Navier-Stokes equations are fundamental in fluid dynamics, describing the motion of incompressible viscous fluids. Their analysis is critical for understanding turbulence, stability, and flow ...

For functions f ∈ L1(Rn) we consider extensions to Rn × R+ given by convolving f with an approximate identity. For a large class of approximate identities we obtain a Fatou-type theorem where the ...

During my time as an eager undergraduate mathematician, I’d often wonder what it would feel like to prove a truly new result and have my name immortalised in the mathematical history books. I thought ...