Stability of trigonometric approximation in $$L^p$$ and applications to prediction theory

Abstract Let $$\Gamma $$ Γ be an LCA group and $$(\mu _n)$$ ( μ n ) a sequence of bounded regular Borel measures on tending to measure $$\mu _0$$ 0 . G the dual , S non-empty subset $$G \setminus \{ 0 \}$$ G \ { } $$[{\mathcal T}(S)]_{\mu _n,p}$$ [ T S ] , p subspace $$L^p(\mu L $$p \in (0,\infty )$$ ∈ ∞ spanned by characters which are generated elements The limit behaviour metric projections function 1 onto as well corresponding approximation errors studied. results applied obtain stability theorems for prediction weakly stationary or harmonizable symmetric p -stable stochastic processes. Along with general problem particular cases linear interpolation extrapolation finite periodic observation set studied in detail compared each other.