On the set of all continuous functions with uniformly convergent Fourier series

Nonanalytic Functions of Absolutely Convergent Fourier Series.

On the Summation of a Particular Non-uniformly-convergent Series

In a previous article the force between a dielectric cylinder and a conducting half-space for the cylinder approaching the half-space was obtained as the limit of a non-uniformly-convergent series. A special asymptotic analysis was performed to get a closed-form solution for this limit. The present article focuses on a delicate and crucial step in this analysis and gives a justification by a ma...

The Existence of Nonabsolutely Convergent Fourier Series on Compact Groups

1. J. W. S. Cassels, An introduction to diophantine approximation, Cambridge University Press, 1959, Chapter IV, §5. 2. J. F. Koksma, Diophantische Approximationen, Ergebnisse der Mathematik, vol. IV, Berlin, Springer, 1937, Chapter VIII, §3. 3. G. M. Petersen, Almost convergence and uniformly distributed sequences, Quart. J. Math. vol. 7 (1956) pp. 188-191. 4. H. Weyl, Uber die Gleichverteilun...

Rings of Uniformly Continuous Functions

There is a natural bijective correspondence between the compactifications of a Tychonoff space X, the totally bounded uniformities on X, and the unital C∗-subalgebras of C∗(X) (the algebra of bounded continuous complex valued functions on X) with what we call the completely regular separation property. The correspondence of compactifications with totally bounded uniformities is well know and ca...

Functions on circles : Fourier series

1. Provocative example 2. Natural function spaces on the circle S = R/2πZ 3. Topology on C∞(S1) 4. Pointwise convergence of Fourier series 5. Distributions: generalized functions 6. Invariant integration, periodicization 7. Hilbert space theory of Fourier series 8. Levi-Sobolev inequality, Levi-Sobolev imbedding 9. C∞(S1) = limC(S) = limH(S) 10. Distributions, generalized functions, again 11. T...