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Determination of the Jumps of a Bounded Function by Its Fourier Series

โœ Scribed by George Kvernadze

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
410 KB
Volume
92
Category
Article
ISSN
0021-9045

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โœฆ Synopsis

The well-known identity which determines the jumps of a function of bounded variation by its Fourier series is extended to larger classes of functions, such as V 8 , 4BV, and V[v], under some conditions on the generalized variations. It is shown as well that the conditions on the generalized variations are definitive in some sense. Based on the above-mentioned results, an identity which determines the jumps of a bounded function by its Fourier series with respect to the system of generalized Jacobi polynomials is obtained for these function classes. 1998 Academic Press is the modulus of continuity of f # C[a, b] on [a, b]. If g # L[&?, ?], g has a Fourier series with respect to the trigonometric system [1, cos n%, sin n%] n=1 , and we denote the nth partial sum of the Article No. AT973125 167

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