In this work, we calculate the tensor power spectrum and the tensor-to-scalar ratio [Formula: see text] within the frame of the Starobinsky inflationary model using the improved uniform approximation method and the third-order phase-integral method. We compare our results with those obtained with numerical integration and the slow-roll approximation to second-order. We have obtained consistent values of [Formula: see text] using the different approximations, and [Formula: see text] is inside the interval reported by observations.
We introduce new reproducing kernel Hilbert spaces on a trapezoidal
semi-infinite domain $B_{\infty}$ in the plane. We
establish uniform approximation results in terms of the number of nodes
on compact subsets of $B_{\infty}$ for solutions to
nonhomogeneous hyperbolic partial differential equations in one of these
spaces,
$\widetilde{W}(B_{\infty})$.
Furthermore, we demonstrate the stability of such solutions with respect
to the driver. Finally, we give an example to illustrate the efficiency
and accuracy of our results.
AbstractThe aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences $u_{m} $
u
m
and $v_{m}$
v
m
of functions. We prove that the new operators provide better weighted uniform approximation over $[0,\infty )$
[
0
,
∞
)
. In terms of weighted moduli of smoothness, we obtain degrees of approximation associated with the function ρ. Also, we prove Voronovskaya-type theorem, quantitative estimates for the local approximation.
<p style='text-indent:20px;'>In this paper, we introduce frames with the uniform approximation property (UAP). We show that with a UAP frame, it is efficient to recover a signal from its frame coefficients with one erasure while the recovery error is smaller than that with the ordinary recovery algorithm. In fact, our approach gives a balance between the recovery accuracy and the computational complexity.</p>
Semiclassical analysis of the tensor power spectrum in the Starobinsky inflationary model
