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Theory of Approximation of Functions of a Real Variable
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THE BEST APPROXIMATION
This chapter explains the best approximation by polynomials on a finite segment. In the determination of the best approximation of functions, it would be possible in place of the closed boundedExpand
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WEIERSTRASS'S THEOREM
This chapter provides an overview of Weierstrass's theorem. The basis of the theory of approximation of functions of a real variable is a theorem discovered by Weierstrass that is of great importanceExpand
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CONVERSE THEOREMS. CONSTRUCTIVE CHARACTERISTICS OF SOME CLASSES OF FUNCTIONS
This chapter discusses differential properties of functions with a given sequence of best Approximations, It is possible in some cases to give a complete description in terms of the bestExpand
Deformation of Metric Spaces and Some Related Problems of the Theory of Functions
CONTENTSPreface ??1. Statement of the problem, physical interpretation and fundamental result ??2. The space consisting of a finite number of elements. Problem of the deviation of polyhedra ??3. SomeExpand
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SOME PROPERTIES OF ALGEBRAIC POLYNOMIALS AND TRANSCENDENTAL INTEGRAL FUNCTIONS OF EXPONENTIAL TYPE
This chapter discusses the properties of algebraic polynomials and transcendental integral functions of exponential type. Among all possible distributions of the points x 0 , x l …, x nExpand
Exact constants in some converse theorems for approximations by trigonometric polynomials
It is known that if the continuous 2π-periodic function f(x) belongs to the class w(r) (r=1, 2, ...), i.e., it has an absolutely continuous derivative of order r—1 such that we have almost everywhere
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LINEAR PROCESSES OF APPROXIMATION OF FUNCTIONS BY POLYNOMIALS AND SOME ESTIMATES CONNECTED WITH THEM
This chapter explains the linear processes of approximation of functions by polynomials and some estimates connected with them. The exact determination of polynomials is successfully achieved when FExpand
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