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Frontmatter -- Contents -- Preface to the English Edition -- Preface to the Russian Edition -- Introduction -- Chapter 1. SIMPLEST EXTREMAL PROBLEMS -- Chapter 2. APPROXIMATION OF FUNCTIONS OF ONE VARIABLE BY FOURIER SUMS -- Chapter 3. APPROXIMATION OF FUNCTIONS OF MANY VARIABLES BY FOURIER SUMS -- Chapter 4. FEJER SUMS -- Chapter 5. SPHERICAL RIESZ SUMS -- Chapter 6. ROGOSINSKI SUMS -- Chapter 7. FAVARD SUMS -- REFERENCES -- SUBJECT INDEX

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The theory of approximation of functions is one of the central branches in mathematical analysis and has been developed over a number of decades. This monograph deals with a series of problems related to one of the directions of the theory, namely, the approximation of periodic functions by trigonometric polynomials generated by linear methods of summation of Fourier series. More specificly, the following linear methods are investigated: class...