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Classification and Approximation of Periodic Functions (Paperback, Softcover reprint of the original 1st ed. 1995)
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Classification and Approximation of Periodic Functions (Paperback, Softcover reprint of the original 1st ed. 1995)
Series: Mathematics and Its Applications, 333
Expected to ship within 10 - 15 working days
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The chapters are split into sections, which, in turn, are split
into subsections enumerated by two numbers: the first stands for
the number of the section while the second for the number ofthe
subsection itself. The same numeration is used for all kinds of
statements and formulas. If we refer to statements or formulas in
other chapters, we use triple numeration where the first number
stands for the chapter and the other two have the same sense. The
results presented in this book were discussed on the seminars at
the Institute of Mathematics of Ukrainian Academy ofSciences, at
the Steklov Mathematical Institute of the Academy of Sciences of
the USSR, at Moscow and Tbilisi State Universities. I am deeply
grateful to the heads of these seminars Professors V. K. Dzyadyk,
N. P. Kor- neichuk, S. B. Stechkin, P. L. U1yanov, and L. V.
Zhizhiashvili as well as to the mem- bers ofthese seminars that
took an active part in the discussions. In TRODUCTIon It is well
known for many years that every 21t -periodic summable function
f(x) can be associated in a one-to-one manner with its Fourier
series (1. 1) Slfl where I It = - f f(t)cosktdt 1t -It and I It - f
f(t)sinktdt. 1t -It Therefore, if for approximation of a given
function f(*), it is necessary to construct a sequence
ofpolynomials Pn (.
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