To check that an object is of this class, use functions is.Lfd
or int2Lfd.
Linear differential operator objects are often used to define
roughness penalties for smoothing towards a "hypersmooth" function that
is annihilated by the operator. For example, the harmonic acceleration
operator used in the analysis of the Canadian daily weather data
annihilates linear combinations of $1, sin(2 pi t/365)$ and $cos(2 pi
t/365)$, and the larger the smoothing parameter, the closer the smooth
function will be to a function of this shape.
Function pda.fd estimates a linear differential operator object
that comes as close as possible to annihilating a functional data
object.
A linear differential operator of order $m$ is a linear combination of
the derivatives of a functional data object up to order $m$. The
derivatives of orders 0, 1, ..., $m-1$ can each be multiplied by a
weight function $b(t)$ that may or may not vary with argument $t$.
If the notation $D^j$ is taken to mean "take the derivative of order
$j$", then a linear differental operator $L$ applied to function $x$
has the expression
$Lx(t) = b_0(t) x(t) + b_1(t)Dx(t) + ... + b_{m-1}(t) D^{m-1} x(t)
+ D^mx(t)$
There are print, summary, and plot methods for
objects of class Lfd.