Sentence examples for acting on functions from inspiring English sources
Given a Riemannian manifold ((M^n,g)), with a Riemannian smooth volume form expressed in local coordinates ((x_1,ldots,x_n)) as (d vol= sqrt{g} dx_1 ldots dx_n), one can consider the corresponding heat operator acting on functions (u Mrightarrow mathbb {R}), begin{aligned} L_gu = partial _t u - frac{1}{sqrt{g}} sum _{i,j=1}^n partial _i left( sqrt{g} g^{ij} partial _j uright).
acting on functions defined on the entire space R n.
The commutator of two such fields (considered as derivations acting on functions) is again left-invariant, and defines the Lie bracket on ({T}_e G).
In 2008, J. Parcet showed the (1,1) weak-boundedness of Calderón Zygmund operators acting on functions taking values in a von Neumann algebra.
These are sharp generalizations of Cheeger Colding's spectral convergence of the Laplacian acting on functions to the cases of tensor fields and differential forms.
acting on functions defined on the space R n, satisfies the inequalities 0 < M 1 | ξ | 2 m ≤ ( − 1 ) m B t, x ≤ M 2 | ξ | 2 m < ∞ (53).
In this paper we develop a theory of singular integral operators acting on function spaces over the measured metric space (Rd,ρ,γ), where ρ denotes the Euclidean distance and γ the Gauss measure.
This finally allows us to introduce X, R, L as linear operators acting on all complex-valued functions which have compact support on the grid Ω = { r q k ∣ k ∈ Z } ∪ { − s q k ∣ k ∈ Z }. (33).
Through sequential step change of set points, the coupled closed-loop TITO system is decoupled equivalently into four independent single open-loop processes with same input signal acting on the four transfer functions.
The role of Dof TFs, a group of plant-specific TFs, recently emerged as part of the transcriptional regulatory networks acting on the formation and functioning of the vascular tissues.
The Landau de Gennes model of liquid crystals is a functional acting on wave functions (order parameters) and vector fields (director fields).
