S M Shah
Articles written in Proceedings – Section A
Volume 2 Issue 4 October 1935 pp 321-332
Volume 21 Issue 4 April 1945 pp 162-164
Volume 28 Issue 6 December 1948 pp 519-526
Volume 36 Issue 5 November 1952 pp 402-404
Volume 65 Issue 4 April 1967 pp 227-232
If the partial sums of a trigonometric series are non-negative and two additional conditions are satisfied, then the given series is a Fourier series. One of these conditions is analysed here and necessary expansions and numerical values are given.
Volume 80 Issue 4 October 1974 pp 161-167
A result of Singh and Sreenivasulu is proved under less restrictive hypothesis. It is also shown that if a condition on the coefficients is not satisfied, the theorem will not hold.