Determination of Function by its Fourier Series. Notes on Fourier Analysis (XII)

Determination of a jump by Fourier and Fourier-Chebyshev series

‎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 ...

Notes on Fourier Series

A function or a real variable f is said to be periodic with period P if f(x+ P ) = f(x) holds for all x. Hence, if we know the values of f on an interval of length P , we know its values everywhere. If f is a function defined on an interval [a, b), we can extend f to a function defined for all x which is periodic of period b− a. We simply define f(x) to be f(x+ n(b− a)), where n is the integer ...

Some notes on L-projections on Fourier-Stieltjes algebras

In this paper, we investigate the relation between L-projections and conditional expectations on subalgebras of the Fourier Stieltjes algebra B(G), and we will show that compactness of G plays an important role in this relation.

Montréal Notes on Quadratic Fourier Analysis

These are notes to accompany four lectures that I gave at the School on additive combinatorics, held in Montréal, Québec between March 30th and April 5th 2006. My aim is to introduce “quadratic fourier analysis” in so far as we understand it at the present time. Specifically, we will describe “quadratic objects” of various types and their relation to additive structures, particularly four-term ...

Linear and Nonlinear Analysis of Cable Stayed Bridges By Fourier Series