Calculation of the Reproducing Kernel on the Reproducing Kernel Space with Weighted Integral

Er Gao; Songhe Song; Xinjian Zhang
January 2012
Journal of Applied Mathematics;2012, p1
Academic Journal
We provide a new definition for reproducing kernel space with weighted integral and present a method to construct and calculate the reproducing kernel for the space. The new reproducing kernel space is an enlarged reproducing kernel space, which contains the traditional reproducing kernel space. The proposed method of this paper is a universal method and is suitable for the case of that the weight is variable. Obviously, this new method will generalize a number of applications of reproducing kernel theory to many areas.


Related Articles

  • Calculation of Some Integrals Arising in the Samara-Valencia Solution for Dry Flat Grinding. González-Santander, J. L. // Mathematical Problems in Engineering;8/11/2015, Vol. 2015, p1 

    In the framework of the Samara-Valencia solution for heat transfer in grinding, two nontabulated integrals involving Macdonald’s function of zeroth order are calculated.

  • Review on loop integrals which need regularization but yield finite results. Weinzierl, Stefan // Modern Physics Letters A;May2014, Vol. 29 Issue 15, p1 

    In this pedagogical paper I will discuss one-loop integrals, where (i) different regions of the integration region lead to divergences and (ii) where these divergences cancel in the sura over all regions. These integrals cannot be calculated without regularization, in spite of the fact that they...

  • NUMERICAL CALCULATION WITH ARBITRARY PRECISION. RODRIGUES, B. O.; DA MOTA, L. A. C. P.; DUARTE, L. G. S. // International Journal of Modern Physics E: Nuclear Physics;Oct2007, Vol. 16 Issue 9, p3045 

    The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and rounding errors may induce the user to incorrect...

  • Reproducing Kernel Space Method for the Solution of Linear Fredholm Integro-Differential Equations and Analysis of Stability. Xueqin Lv; Yue Gao // Abstract & Applied Analysis;2012, p1 

    We present a numerical method to solve the linear Fredholm integro-differential equation in reproducing kernel space. A simple algorithm is given to obtain the approximate solutions of the equation. Through the comparison of approximate and true solution, we can find that the method can...

  • Solving Singularly Perturbed Multipantograph Delay Equations Based on the Reproducing Kernel Method. Geng, F. Z.; Qian, S. P. // Abstract & Applied Analysis;2014, p1 

    A numerical method is presented for solving the singularly perturbed multipantograph delay equations with a boundary layer at one end point. The original problem is reduced to boundary layer and regular domain problems. The regular domain problem is solved by combining the asymptotic expansion...

  • Analytical realization of finite-size scaling for Anderson localization. Does the band of critical states exist for d > 2? Suslov, I. // Journal of Experimental & Theoretical Physics;Jun2006, Vol. 102 Issue 6, p938 

    An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1 D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that the Anderson transition point splits into the band of...

  • CALCULATING ZEROS OF THE SECOND KIND (h, q)-BERNOULLI POLYNOMIALS. RYOO, C. S. // Neural, Parallel & Scientific Computations;Sep-Dec2012, Vol. 20 Issue 3/4, p271 

    In [11], we observed the behavior of real roots of the second kind Bernoulli polyno- mials. The main purpose of this paper is to investigate the zeros of the second kind (h, q)-Bernoulli polynomials B(h)n, q(x) for -1 < q < 0. Furthermore, we give a table for the solutions of the second kind (h,...

  • Analysing algorithm for the cinematic unevennesses at the gear processing. Simionescu, Cristian // Annals. Computer Science Series;2010, Vol. 8 Issue 1, Special section p182 

    The aim of the present paper is to analyze the cinematic unevennesses. Tooth generation by envelope curve inserts profile errors that are independent on tooth charging. It is proposed a mathematic calculus model in order to get the profile error inserted by envelope curve tooth generation. The...

  • COMPUTATIONAL ASPECTS OF QUASI-STATIC CRACK PROPAGATION. KNEES, DOROTHEE; SCHRÖDER, ANDREAS // Discrete & Continuous Dynamical Systems - Series S;Feb2013, Vol. 6 Issue 1, p63 

    The focus of this note lies on the numerical analysis of models describing the propagation of a single crack in a linearly elastic material. The evolution of the crack is modeled as a rate-independent process based on the Griffth criterion. We follow two different approaches for setting up...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics