Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-24T20:54:58.441Z Has data issue: false hasContentIssue false

On the summability of Fourier integrals

Published online by Cambridge University Press:  24 October 2008

M. K. Nayak
Affiliation:
Sutahat, Outtack 1, Orissa, India

Extract

We say a series is summable L if

tends to a finite limit s as x → 1 in the open interval (0, 1) where

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Mohanty, R. and Nanda, M.The summability (L) of the differentiated Fourier series. Quart. J. Math. Oxford (2), 311 (1962), 4044.CrossRefGoogle Scholar
(2)Nanda, M.The summability (L) of the Fourier series and the first differentiated series. Quart. J. Math. Oxford (2), 13 (1962), 229234.CrossRefGoogle Scholar
(3)Hsiang, F. C.Summability (L) of the Fourier series. Bull. Amer. Math. Soc.. 67 (1961), 150153.CrossRefGoogle Scholar
(4)Borwein, P.A logarithmic method of summability J. London Math. Soc. 33 (1958), 212220.CrossRefGoogle Scholar
(5)Rangachri, M. S.A generalization of Abel-type sumniability methods for functions. Indian J. Math. 7 (1965), 1723 and a correction given in Indian J. Math. 8 (1966), 97.Google Scholar
(6)Hardy, G. H.Divergent series (Oxford, 1949).Google Scholar
(7)Hardy, G. H. and Wright, E. M.Theory of number, p. 350 (Oxford, 1938).Google Scholar
(8)Titchmarsh, E. C.Introduction to the theory of Fourier integrals (Oxford, 1937).Google Scholar
(9)Widder, P. V.The Laplace transform, p. 92 (Princeton, 1941).Google Scholar