In this paper, we study the operator Ro(f, z) and obtain that Ro(f, z) doesn't converge to f(z)∈A(|z|≤1) in the sence of mean convergence in the space L_p(|z|=1) (0
For the orthogonal series Σ∞ n=1 a nφ n(x) consist from the normal orthorhombic systems {φ n(x)} ∞ n=1 L p(E),In this paper,We give out the sufficient condition that the coefficients{a n}converge to zero,and we get the corollary on L 2([0,1]).
Suppose X is a real Banach space and H∶X→X is a Lipschitz operator, T∶X→X uniformly continuous with the bounded range and H+T strongly accretive, then the Ishikawa and Mann iterative processes with errors converge strongly to the unique solution of the equation Hx+Tx=f.
设 X是实 Banach空间 ,H∶ X→ X是 L ipschitz算子 ,T∶ X→ X是值域有界且一致连续的算子 ,H + T是强增生算子 ,则具有误差项的 Ishikawa和 Mann迭代序列强收敛到方程 H x + Tx =f的唯一解 .
Suppose that X is a real Banach space, H:X→X is Lipschitz operator, T:X→X is uniformly continuous with bounded range, H+T is strongly accretive. Then Mann and Ishikawa iterative processes converge strongly, almost stably, to the unique solution of the equation Hx+Tx=f.
In this paper,we study the convergence by the generalized Hermite Fejer interpolating polynomials on the complex plane,and we obtain the order of approximation that the polynomials converge to f(z)∈A(|z|≤1) in the sense of mean in the space l p (|z|=1)(0
A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener's algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means.
A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener's algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means.
By producing a L2 convergent Neumann series, we prove the invertibility of the elastostatics and hydrostatics boundary layer potentials on arbitrary Lipschitz domains with small Lipschitz character and 3D polyhedra with large dihedral angles.
When a function does not belong to such a space, the sampling series may converge, not to the object function but to an "alias" of it, and an aliasing error is said to occur.
In addition, if the scaling functions have at least asymptotic linear phase, then we prove that they converge to the "sinc" function and their corresponding orthonormal wavelets converge to the "difference" of two sinc functions.
Moreover, we use the Carleson-Hunt theorem to show that the Gabor expansions of Lp functions converge to the functions almost everywhere and in Lp for 1>amp;lt;p>amp;lt;∞.
Our main results relate the convergence of the chromatic expansions to the asymptotic behavior of the coefficients appearing in the three term recurrence satisfied by the corresponding family of orthogonal polynomials PMn(ω).
In this paper, we prove the convergence of the nodal expansion method, a new numerical method for partial differential equations and provide the error estimates of approximation solution.
With almost the same but somewhat more relaxed constraints on the multiple splittings, we prove the convergence and estimate the convergence rate of the new method.