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71.
72.
The paper presents an error-free algorithm to solve a system of linear equations with polynomial coefficients. Modular arithmetic in residual polynomial class and in residual numeric class is employed. The algorithm is iterative and well suited for implementation for computers with vector operations and fast and error-free convolutors.  相似文献   
73.
Let p(z) be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of p(Rz)-βp(rz) + α (R+1/r+1)n-|β | p(rz) s on p(z) s for every α, β∈ C with |α|≤ 1, |β | ≤ 1, R > r 1, and s > 0. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.  相似文献   
74.
75.
In this paper we study spectral sets which are unions of finitely many intervals in R. We show that any spectrum associated with such a spectral set Ω is periodic, with the period an integral multiple of the measure of Ω. As a consequence we get a structure theorem for such spectral sets and observe that the generic case is that of the equal interval case.  相似文献   
76.
The restriction principle is used to implement a realization of the holomorphic representations of SL(2,R) on L 2 (R +,t dt) by way of the standard upper half plane realization. The resulting unitary equivalence establishes a correspondence between functions that transform according to the character ei(2n++1); under rotations and the Laguerre polynomials. The standard recursion relations amongst Laguerre polynomials are derived from the action of the Lie algebra.  相似文献   
77.
78.
In this paper, we further develop the left-definite and right-definite spectral theory associated with the self-adjoint differential operator A in L2(-1,1), generated from the classical second-order Legendre differential equation, having the sequence of Legendre polynomials as eigenfunctions. Specifically, we determine the first three left-definite spaces associated with the pair (L2(-1,1),A). As a consequence of these results, we determine the explicit domain of both the associated left-definite operator A1, first observed by Everitt, and the self-adjoint operator A1/2. In addition, we give a new characterization of the domain D(A) of A and, as a corollary, we present a new proof of the Everitt-Mari result which gives optimal global smoothness of functions in D(A).  相似文献   
79.
This paper is devoted to the study of the approximation properties of linear operators which are partial Fourier--Legendre sums of order n with 2r terms of the form k=1 2r akPn+k(x) added; here P m(x) denotes the Legendre polynomial. Due to this addition, the linear operators interpolate functions and their derivatives at the endpoints of the closed interval [-1,1], which, in fact, for r= = 1 allows us to significantly improve the approximation properties of partial Fourier--Legendre sums. It is proved that these operators realize order-best uniform algebraic approximation of the classes of functions and A q (B). With the aim of the computational realization of these operators, we construct their discrete analogs by means of Chebyshev polynomials, orthogonal on a uniform grid, also possessing nice approximation properties.  相似文献   
80.
This note characterizes the denseness of rational systems
in C[−1, 1], where the nonreal poles in {ak}k=1 \[−1, 1] are paired by complex conjugation. This extends an Achiezer's result.  相似文献   
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