Determination of a jump by Fourier and Fourier-Chebyshev series

Authors

M. Avdispahic University of Sarajevo‎, ‎Deaprtment of Mathematics‎, ‎Zmaja od Bosne 33-35‎, ‎71 000 Sarajevo‎, ‎Bosnia and Herzegovina.

Z. Sabanac University of Sarajevo‎, ‎Deaprtment of Mathematics‎, ‎Zmaja od Bosne 33-35‎, ‎71 000 Sarajevo‎, ‎Bosnia and Herzegovina.

Abstract:

‎By observing the equivalence of assertions on determining the jump of a‎ ‎function by its differentiated or integrated Fourier series‎, ‎we generalize a‎ ‎previous result of Kvernadze‎, ‎Hagstrom and Shapiro to the whole class of‎ ‎functions of harmonic bounded variation‎. ‎This is achieved without the finiteness assumption on‎ ‎the number of discontinuities‎. ‎Two results on determination of jump‎ ‎discontinuities by means of the tails of integrated Fourier-Chebyshev series are also derived.

Upgrade to premium to download articles

Already have an account?login

similar resources

Discrete–time Fourier Series and Fourier Transforms

We now start considering discrete–time signals. A discrete–time signal is a function (real or complex valued) whose argument runs over the integers, rather than over the real line. We shall use square brackets, as in x[n], for discrete–time signals and round parentheses, as in x(t), for continuous–time signals. This is the notation used in EECE 359 and EECE 369. Discrete–time signals arise in t...

full text

Discrete–time Fourier Series and Fourier Transforms

full text

Fourier Series

for some fixed τ , which is called the period of f . Though function approximation using orthogonal polynomials is very convenient, there is only one kind of periodic polynomial, that is, a constant. So, polynomials are not good for approximating periodic functions. In this case, trigonometric functions are quite useful. A large class of important computational problems falls under the category...

full text