The phrase "a linear functional of" is correct and usable in written English.
It is typically used in mathematical contexts, particularly in functional analysis, to describe a specific type of function that maps vectors to scalars.
Example: "In this study, we will explore the properties of a linear functional of the vector space."
Alternatives: "a linear mapping of" or "a linear transformation of".
We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly linear regression.
In this paper estimation of a linear functional of the indirectly observed regression function is considered, when a deterministic design is used.
A linear functional of a Gaussian field is a Gaussian variable.
If F : X ⟶ R is a linear functional of a unit norm defined on the normed linear space X endowed with the norm ∥ ⋅ ∥ and the vectors x 1, …, x n satisfy the condition 0 ≤ r ≤ F ( x i ), i ∈ { 1, …, n }. then r ∑ i = 1 n ∥ x i ∥ ≤ ∥ ∑ i = 1 n x i ∥, where equality holds if and only if both F ( ∑ i = 1 n x i ) = r ∑ i = 1 n ∥ x i ∥. and F ( ∑ i = 1 n x i ) = ∥ ∑ i = 1 n x i ∥.
Any Raman detector signal SRaman is a linear functional of LRaman.
A distribution is a linear functional on of infinitely differentiable functions on with compact supports such that for every compact set there exist constants and satisfying (2.1).
It is independent of the choice of unitary basis and defines a linear functional on the space (C_1) of operators of trace class.
As a distribution, the Dirac delta is a linear functional on the space of test functions and is defined by \delta[\varphi] = \varphi(0)\, for every test function φ.
Recall that a distribution u is a linear functional on C c ∞ ( R ) of infinitely differentiable functions on ℝ with compact supports such that for every compact set K ⊂ R, there exist constants C > 0 and N ∈ N 0 satisfying | 〈 u, φ 〉 | ≤ C ∑ | α | ≤ N sup | ∂ α φ |. for all φ ∈ C c ∞ ( R ) with supports contained in K.
Recall that a distribution u is a linear functional on C c ∞ ( ℝ m ) of infinitely differentiable functions on ℝ m with compact supports such that for every compact set K ⊂ ℝ m there exist constants C > 0 and N ∈ ℕ0 satisfying ∣ 〈 u, φ 〉 ∣ ≤ C ∑ ∣ α ∣ ≤ N sup ∣ ∂ α φ ∣. for all φ ∈ C c ∞ ( ℝ m ) with supports contained in K.
The direct meshless local Petrov Galerkin method is a newly developed modification of the meshless local Petrov Galerkin method that any linear functional of moving least squares approximation will be only done on its basis functions.
