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61.
Josef Obermaier 《Journal of Approximation Theory》2003,125(2):303-312
Let
be compact with #S=∞ and let C(S) be the set of all real continuous functions on S. We ask for an algebraic polynomial sequence (Pn)n=0∞ with deg Pn=n such that every fC(S) has a unique representation f=∑i=0∞ αiPi and call such a basis Faber basis. In the special case of
, 0<q<1, we prove the existence of such a basis. A special orthonormal Faber basis is given by the so-called little q-Legendre polynomials. Moreover, these polynomials state an example with A(Sq)≠U(Sq)=C(Sq), where A(Sq) is the so-called Wiener algebra and U(Sq) is the set of all fC(Sq) which are uniquely represented by its Fourier series. 相似文献
62.
用无限阶Toeplitz矩阵求常系数微分方程的级数解 总被引:1,自引:0,他引:1
无限阶Toeplitz矩阵的属于0的特征向量可递推地求得,可表示常系数齐次微分方程的解.用它的逆可求得常系数非齐次微分方程的特解. 相似文献
63.
U. Goginava 《分析论及其应用》2007,23(3):255-265
In this paper we prove that iff ∈ C([-π,π]2) and the function f is bounded partial p-variation for some p ∈ [1, ∞), then the double trigonometric Fourier series of a function f is uniformly (C;-α,-β) summable (α β< 1/p,α,β> 0) in the sense of Pringsheim. If α β≥ 1/p, then there exists a continuous function f0 of bounded partial double trigonometric Fourier series of fo diverge over cubes. 相似文献
64.
A. G. García M. A. Hernndez-Medina 《Journal of Mathematical Analysis and Applications》2003,280(2):221-231
The close relationship between discrete Sturm–Liouville problems belonging to the so-called limit-circle case, the indeterminate Hamburger moment problem and the search of self-adjoint extensions of the associated semi-infinite Jacobi matrix is well known. In this paper, all these important topics are also related with associated sampling expansions involving analytic Lagrange-type interpolation series. 相似文献
65.
66.
Periodica Mathematica Hungarica - 相似文献
67.
Richard Arratia Bla Bollobs Gregory B. Sorkin 《Journal of Combinatorial Theory, Series B》2004,92(2):199-233
Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable “interlace polynomial” for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and fuse reduction characterizing the Tutte polynomial.It emerges that the interlace graph polynomial may be viewed as a special case of the Martin polynomial of an isotropic system, which underlies its connections with the circuit partition polynomial and the Kauffman brackets of a link diagram. The graph polynomial, in addition to being perhaps more broadly accessible than the Martin polynomial for isotropic systems, also has a two-variable generalization that is unknown for the Martin polynomial. We consider extremal properties of the interlace polynomial, its values for various special graphs, and evaluations which relate to basic graph properties such as the component and independence numbers. 相似文献
68.
Condition monitoring and life prediction of the vehicle engine is an important and urgent problem during the vehicle development process. The vibration signals that are closely associated with the engine running condition and its development trend are complex and nonlinear. The chaos theory is used to treat the nonlinear dynamical system recently. A novel chaos method in conjunction with SVD (singular value decomposition)denoising skill are used to predict the vibration time series. Two types of time series and their prediction errors are provided to illustrate the practical utility of the method. 相似文献
69.
从等离子体平板显示器(PDP)的发光原理出发,分析和研究了存贮控制电路的工作原理,提出基于FPGA的电路设计方案,并给出数据整理电路和驱动信号产生电路的具体电路框图,最后给出部分仿真波形. 相似文献
70.
Eero Immonen 《Journal of Mathematical Analysis and Applications》2004,300(1):79-101
In this article, we study the effect of the chosen representation of a point value (and point evaluation) on the class of periodic signals realizable using a certain type of infinite-dimensional linear system. By suitably representing the point evaluation at the origin in a Hilbert space, we are able to give a complete characterization of its extensions. These extensions involve a new concept called δ-sequence, the use of which as an observation operator of an infinite-dimensional linear system is studied in this article. In particular, we consider their use in the realization of periodic signals. We also investigate how the use of δ-sequences affects the convergence properties of such realizations; we consider the rate and character of convergence and the removal of the Gibbs phenomenon. As still a further demonstration of the significance of the chosen concept of a point value, we discuss the use of distributional point values in the realization of periodic distributions. The possible applications of this work lie in regulator problems of infinite-dimensional control theory, as is indicated by the well-known internal model principle. 相似文献