Let us define now a class of weighted Sobolev spaces, with a weight function of the above-mentioned type.
Weighted distribution of discrete normal with parameter (λ, q) with weight function of the form π x is again discrete normal (πλ, q).
The method is based on the weight function of a single crack.
where W ω,y) is the weight function of the antenna cell at the position y.
The weight function of each method is described in the following subsection.
Conceptually, it is due to the fact that the weight function of this method is simple.
Theorem 2.3 Let 1 p 1 + 1 p 2 = 1 p 3, p 3 ≥ 1 and υ s ( x ) = ( 1 + | x | ) s, s ≥ 0 be a weight function of polynomial type such that υ s ≤ ω 1.
Then, we can assign a surjective function (h : {1,2, ldots,N} rightarrow U) as a weight function of elements in F where (h(i) in U) is considered as the weight of (F_i).
This paper presents a revised procedure for computation of double-K fracture parameters of concrete split-tension cube specimen using weight function of the centrally cracked plate of finite strip with a finite width.
Under certain conditions on the weight function of the form of a power function, sufficient conditions for the basicity of this system are obtained in generalized weighted Lebesgue space.
In [16] the author considered the weight function of the form ρ ( x ) = { α 2 ; Im α ≠ 0, 0 ≤ x ≤ a < π, 1 ; a < x ≤ π, and the spectra were both continuous and discrete as in our problem.
