1. CMB 2011 (vol 56 pp. 326)
|Restricting Fourier Transforms of Measures to Curves in $\mathbb R^2$|
We establish estimates for restrictions to certain curves in $\mathbb R^2$ of the Fourier transforms of some fractal measures.
Keywords:Fourier transforms of fractal measures, Fourier restriction
2. CMB 2009 (vol 53 pp. 295)
|The Global Attractor of a Damped, Forced Hirota Equation in $H^1$|
The existence of the global attractor of a damped forced Hirota equation in the phase space $H^1(\mathbb R)$ is proved. The main idea is to establish the so-called asymptotic compactness property of the solution operator by energy equation approach.
Keywords:global attractor, Fourier restriction norm, damping system, asymptotic compactness
Categories:35Q53, 35B40, 35B41, 37L30
3. CMB 2005 (vol 48 pp. 260)
|A Restriction Theorem for a \\$k$-Surface in $\mathbb R ^n$ |
We establish a sharp Fourier restriction estimate for a measure on a $k$-surface in $\mathbb R ^n$, where $n=k(k+3)/2$.