Every translation invariant positive definite Hermitian bilinear functional on the Gel'fand-Shilov space sMpMp(ℝn×nK) of general type S is of the form B(ϕ,ψ) = ∫ϕ(x)ψ(x)dμ(x), ϕ, ψ ∈ sMpMp (ℝn), where μ is a positive {M}-tempered measure, i.e., for every ∈ > 0 ∫exp[-M(∈|x|)] dμ(x) < ∞. To prove this we prove Schwartz kernel theorem for {M}-tempered ultradistributions and need Bochner-Schwartz theorem for {M}-tempered ultradistributions. Our result includes most of the quasianalytic cases. Also, we obtain parallel results for the case of Beurling type (Mp.