On the Best Approximation by Trigonometric Polynomials on Convolution Classes of Analytic Periodic Functions

For a continuous $2\pi$-periodic real-valued function $K(t)$, whose amplitudes decrease as a geometric progression with a denominator $q\in(0,1)$ starting from a given number $n\in\mathbb{N}$, we find sharp upper bounds for $q$ ensuring that $K(t)$ satisfies the Nagy condition $N_n^*$.