Sentence examples for bounded function supported on from inspiring English sources

where λ i for i = 1, 2 is a real number, | h i | H atb 1, ∞, 0 = λ 1 + λ 2, a i for i = 1, 2 is a bounded function supported on some cubes Q i ⊂ R and it satisfies ∥ a i ∥ L ∞ ≤ [ μ ( 4 Q i ) S Q i, R ] − 1. (2.2).

where λ i for i = 1, 2, is a real number, | h | H atb 1, ∞ = | λ 1 | + | λ 2 |, a i for i = 1, 2, is a bounded function supported on some cube Q i ⊂ R and it satisfies ∥ a i ∥ L ∞ ≤ [ μ ( 4 Q i ) S Q i, R ] − 1. (2.2).

1.9 allow us to prove that if f is a bounded function on ({mathbb R}^3) with compactly supported Fourier transform, then (mathfrak {D}_1f) and (mathfrak {D}_3f) do belong to the space of Schur multipliers (mathfrak {M}_{{mathbb R}^3,{mathbb R}^3}).

Let f be a bounded function on ({mathbb R}) whose Fourier transform is supported in ([0,sigma ]).

Let f be a bounded function on ({mathbb R}) whose Fourier transform is supported in ([-sigma,sigma ]).

Let f be a bounded function on ({mathbb R}^2) whose Fourier transform is supported in ([-sigma,sigma ]times [-sigma,sigma ]).

Let f be a bounded function on ({mathbb R}^2) whose Fourier transform is supported in the ball ({xi in {mathbb R}^2:Vert xi Vert le 1}).

Let f be a bounded function on ({mathbb R}^2) such that its Fourier transform is supported in ({xi in {mathbb R}^2:Vert xi Vert le sigma }), (sigma >0).

As before, it suffices to consider the case when f is a bounded function on ({mathbb R}) whose Fourier transform has compact support in ((0,infty )).

Let f be the function on ({mathbb R}^3) defined by begin{aligned} f(x_1,x_2,x_3)=g(x_1-x_3)sin x_2,quad x_1,x_3in,x_3in {mathbb R}. end{aligned} (1.10.2 Then f is a bounded function on ({mathbb R}^3) whose Fourier transform has compact support, but (mathfrak {D}_2fnot in mathfrak {M}_{{mathbb R}^3,{mathbb R}^3}).

Let F be a Borel bounded function on [−a,a], SpL2T⊂[−a,a].