Derivatives of the L^p cosine transform
| dc.creator | Lonke, Yossi | |
| dc.date | 2001-11-27 | |
| dc.date.accessioned | 2026-07-07T04:44:47Z | |
| dc.date.available | 2026-07-07T04:44:47Z | |
| dc.description | The $L^p$-cosine transform of an even, continuous function $f\in C_e(\Sn)$ is defined by: $$H(x)=\int_{\Sn}|\ip{x}ξ|^pf(ξ) dξ,\quad x\in {\R}^n.$$ It is shown that if $p$ is not an even integer then all partial derivatives of even order of $H(x)$ up to order $p+1$ (including $p+1$ if $p$ is an odd integer) exist and are continuous everywhere in ${\R}^n\backslash\{0\}$. As a result of the corresponding differentiation formula, we show that if $f$ is a positive bounded function and $p>1$ then $H^{1/p}$ is a support function of a convex body whose boundary has everywhere positive Gauss-Kronekcer curvature. | |
| dc.description | LaTeX 14 pages. To appear in `Advances in Mathematics`. Current email address: yossi_lonke@creoscitex.com | |
| dc.identifier | https://arxiv.org/abs/math/0111272 | |
| dc.identifier | http://arxiv.org/abs/math/0111272 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62734 | |
| dc.subject | Metric Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 52A20, 32Q10, 46F10 | |
| dc.title | Derivatives of the L^p cosine transform | |
| dc.type | text |