Recovery of the Laplace–Bessel operator of a function by the spectrum, which is specified not everywhere

In this paper, we present results related to the problem of the best recovery of a fractional power of the $B$-elliptic Laplace–Bessel operator of a smooth function from its Fourier–Bessel transform, which is known exactly or approximately on a certain convex set. The cases of primary estimates in $L_2^\gamma$ and $L_\infty$ are considered.