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21.
22.
The object of the present investigation is to introduce a new trigonometric method of summation which is both regular and
Fourier effective and determine its status with reference to other methods of summation (see §2-§4) and also give an application
of this method to determine the degree of approximation in a new Banach space of functions conceived as a generalized Holder
metric (see §5). 相似文献
23.
24.
J. J. EGOZCUE J. L. DIAZ-BARRERO V. PAWLOWSKY-GLAHN 《数学学报(英文版)》2006,22(4):1175-1182
The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison's ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space. 相似文献
25.
基于傅立叶变换轮廓术的物面相位提取 总被引:1,自引:0,他引:1
采用傅立叶变换轮廓术,针对基频提取的关键技术采用逐行傅立叶变换,准确提取基频信息的方法恢复相位信息.在此基础上,以未畸变条纹为基准,得出被测物体的真实位相值.该方法只需一幅条纹图,节约了测量时间.实验证明可实现无接触面型的自动传感. 相似文献
26.
A. Budhiraja 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2003,39(6):2318-941
In this work we study connections between various asymptotic properties of the nonlinear filter. It is assumed that the signal has a unique invariant probability measure. The key property of interest is expressed in terms of a relationship between the observation σ field and the tail σ field of the signal, in the stationary filtering problem. This property can be viewed as the permissibility of the interchange of the order of the operations of maximum and countable intersection for certain σ-fields. Under suitable conditions, it is shown that the above property is equivalent to various desirable properties of the filter such as
- (a) uniqueness of invariant measure for the signal,
- (b) uniqueness of invariant measure for the pair (signal, filter),
- (c) a finite memory property of the filter,
- (d) a property of finite time dependence between the signal and observation σ fields and
- (e) asymptotic stability of the filter.
27.
Based on the newly constructed two mutually conjugate 3-mode entangled states of continuum variablesin three-mode Fock space we introduce entangled fractional Fourier transform (EFFT) for the tripartite entangled staterepresentations, which are not a direct product of three 1-dimensional FFTs. The eigenmodes of EFFT are obtained,which is different from the usual Hermite polynomials. The EFFT of the three-mode squeezed state is derived. 相似文献
28.
29.
D. Barrios Rolanía G. Lpez Lagomasino E. B. Saff 《Journal of Approximation Theory》2003,124(2):263-281
Using a convergence theorem for Fourier–Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard's theorem for determining the radius of m-meromorphy of a function analytic on the unit disk and apply this to the location of poles of the reciprocal of Szeg
functions. 相似文献