Physical Sciences and Mathematics Commons^™

A Support Theorem For A Wave Equation, Aysha Khaled Alshamsi

Theses

It is well known that the fundamental solution to the classical wave equation Δ𝑢 (𝑥, 𝑡) − ∂_𝑡𝑡𝑢(𝑥,𝑡) = 0 is supported on the light cone {(𝑥, 𝑡) ∈ ℝ^𝑛× ℝ : ||𝑥|| = |𝑡|} if and only if the dimension 𝑛 is odd and ≥ 3. Because we are living in a 3-dimensional world we can hear each other clearly; One has a pure propagator without residual waves. In this thesis we consider the wave equation

2||𝑥||Δ_𝑘𝑢_𝑘(𝑥, 𝑡) − ∂_𝑡𝑡𝑢(𝑥,𝑡) = 0, (𝑥, 𝑡) ∈ ℝ^𝑛 × ℝ …

On The Generalized Hardy-Littlewood Maximal Operator, Namarig Hashim Hassan

Theses

No abstract provided.