Sentence examples for be the integral operator from inspiring English sources

Let T be the integral operator as defined in Definition.

Let T be the integral operator as Definition 1, the sequence { C k } ∈ l 1.

Theorem 1 Let T be the integral operator as defined in Definition, 0 < δ < 1 and b ∈ BMO ( R n ).

Lemma 6 Let T be the integral operator as Definition 1, 0 ≤ η < n, 0 < D < 2 n and 1 ≤ p < ∞.

Theorem 1 Let T be the integral operator as Definition 1, the sequence { C k } ∈ l 1, 0 < β < 1, q ′ ≤ s < ∞ and b ∈ Lip β ( R n ).

Theorem 7 Let T be the integral operator as Definition 1, the sequence { k C k } ∈ l 1 and b ∈ B M O ( R n ).

For that, let and be the integral operators defined, respectively, by (3.21).

where is the integral operator defined by (2.29).

We note that, formally, the identity (2.8) can be rewritten as relation (1.6) where A is the "integral operator" with kernel v b v.

where I α, β, p β + 2 + i, δ ϕ, φ is the integral operator defined by (1) with γ = p β + 2 + i.

Let us find the expression of the operator R λ 2 ( A ). Lemma 8 The resolvent R λ 2 ( A ) is the integral operator with the kernel G ( x, t ; λ ) = − 1 Δ { φ ( t, λ ) ψ ( x, λ ), t ≤ x, ψ ( t, λ ) φ ( x, λ ), t ≥ x. (19).