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The Study of Some Operators Approximation and Interpolation Approximation Problems

Author: FengYue
Tutor: WuGaRiDi
School: Inner Mongolia Normal
Course: Basic mathematics
Keywords: Orlicz spaces LMBa space Operator approximation Interpolation Approximation
CLC: O174.41
Type: Master's thesis
Year: 2011
Downloads: 33
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Abstract


Function approximation theory is an important branch of modern mathematics disciplines that began in the 19th century, two famous theorem establish continuous function can be established in 1885 Weierstrass polynomial approximation theorem and Chebyshev in 1859 to establish the most good approximation of the characterization theorem in the discipline of the last century to flourish and become an independent discipline people to use simple computable function approximation generally function on the basis of a series of theories and methods . best approximation , Fourier approximation , trigonometric polynomial approximation , the algebraic polynomial approximation , linear operator approximation , interpolation approximation , rational approximation , reciprocal approximation , and Muntz approximation as more and more complexity of the problem and nonlinear the problem occurs in the a broader function space research is particularly important to approximation theory , the work done in this article is the operator approximation Orlicz space , as well as by an Orlicz space constitute the LMBa of space research , the interpolation approximation and other issues . article is composed of : Preliminaries for the three chapters. chapter introduces the basic knowledge the Orlicz space with LMBa of space . : operator approximation study two different linear operator approximation problem , the approximation Theorem . part of the K-functional and moduli of smoothness tools discussed two generalized Durrmeyer-Bezier count the sub in LMBa space approximation estimated second part of the K-functional aids , through the establishment of Orlicz spaces within Bernstein inequality Shepard operator approximation equivalence theorem in Orlicz space Chapter : interpolation approximation introduces the interpolation approximation problem and get the corresponding approximation theorem , the first part , by means of the relevant conclusions of the literature [ 2 ] to the second category Chebyshev polynomials zero the the interpolation node group intends Grunwald interpolation polynomial approximation in weighted Orlicz spaces degrees . second part , the main research Orlicz space Muntz rational approximation and order approximation Jackson type estimate . third part , first class research amendment rational interpolation approximation in in LM, ωBa space , using the Orlicz norm LMBa space Fan number relations inequalities , its in LM, ωBa , -order approximation in space .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Constructive theory of functions > Approximation Theory
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