Softcover ISBN:  9780821831366 
Product Code:  STEKLO/189 
List Price:  $150.00 
MAA Member Price:  $135.00 
AMS Member Price:  $120.00 
Softcover ISBN:  9780821831366 
Product Code:  STEKLO/189 
List Price:  $150.00 
MAA Member Price:  $135.00 
AMS Member Price:  $120.00 

Book DetailsProceedings of the Steklov Institute of MathematicsVolume: 189; 1991; 234 ppMSC: Primary 11; Secondary 41; 42; 43; 46
This collection consists of ten papers presented at the AllUnion School on Function Theory, held in Dushanbe in August 1986, under the editor's guidance. The book encompasses a wide range of current directions in the metric theory of functions, the theory of approximation of functions, and related parts of mathematical analysis. The papers concern the following topics: extremal properties of functions, representation of functions by series, convergence of multiple Fourier series, approximation of functions by trigonometric polynomials in \(L_p\)metrics, widths of classes of functions, approximation of functions by Fourier sums in systems of characters of zerodimensional compact commutative groups, bilinear approximations of functions, the study of Tchebycheff sets in normed linear spaces, and spline approximation of functions of several variables.
Among the results obtained are: new criteria for convexity of Tchebycheff sets in terms of continuity properties of the metric projection operator; conditions on the character of integrability of a periodic function of several variables under which its Fourier series converges to it in measure; a characterization of representation systems for symmetric spaces in which there are no nonzero continuous functionals.
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This collection consists of ten papers presented at the AllUnion School on Function Theory, held in Dushanbe in August 1986, under the editor's guidance. The book encompasses a wide range of current directions in the metric theory of functions, the theory of approximation of functions, and related parts of mathematical analysis. The papers concern the following topics: extremal properties of functions, representation of functions by series, convergence of multiple Fourier series, approximation of functions by trigonometric polynomials in \(L_p\)metrics, widths of classes of functions, approximation of functions by Fourier sums in systems of characters of zerodimensional compact commutative groups, bilinear approximations of functions, the study of Tchebycheff sets in normed linear spaces, and spline approximation of functions of several variables.
Among the results obtained are: new criteria for convexity of Tchebycheff sets in terms of continuity properties of the metric projection operator; conditions on the character of integrability of a periodic function of several variables under which its Fourier series converges to it in measure; a characterization of representation systems for symmetric spaces in which there are no nonzero continuous functionals.