  In metric of spaces $L_{s}, \ 1\leq s\leq\infty$, we obtain exact in order
estimates of best $m$-term trigonometric approximations of classes of
convolutions of periodic functions, that belong to unit all of space $L_{p}, \
1\leq p\leq\infty$, with generated kernel
$\Psi_{\beta}(t)=\sum\limits_{k=1}^{\infty}\psi(k)\cos(kt-\frac{\beta\pi}{2})$,
$\beta\in \mathbb{R}$, whose coefficients $\psi(k)$ tend to zero not slower
than geometric progression. Obtained estimates coincide in order with
approximation by Fourier sums of the given classes of functions in
$L_{s}$-metric. This fact allows to write down exact order estimates of best
orthogonal trigonometric approximation and trigonometric widths of given
classes.
