On the Absolute Summability of Fourier Integral by Abel-Type Method

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Authors

  • B. K. Ray
     Department of Mathematics, J.K.B.K. College, Cuttack 753007, Orissa ,IN
  • M. Samal
     Department of Mathematics, Ravenshaw College, Cuttack 753003, Orissa ,IN

Abstract

This method of summability (L, α) for any α > - 1 is regular and of Abel-type in the sense that its particular case α = 0 gives rise to Abel or (A) summability ([3], pp. 79-81).

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Published

1976-12-01

How to Cite

Ray, B. K., & Samal, M. (1976). On the Absolute Summability of Fourier Integral by Abel-Type Method. The Journal of the Indian Mathematical Society, 40(1-4), 207–215. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/16626

Issue

Volume 40, Issue 1-4, March-December 1976

Section

Articles

License

Copyright (c) 1976 B. K. Ray, M. Samal

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

CARSLAW, H.S., Introduction to the theory of Fourier series and integrals, Third revised edition (Dover).

COOPER, J.L.B., The absolute Cesaro summability for Fourier integrals, Proc. London Math. Soc. (2) 45 (1939), 425-431.

HARDY, G.H., Divergent series, Oxford, Clarendon Press, 1963.

JAKIMOVSKJ, A., Some remarks on Tauberian Theorems, Quart. J. Math. Oxford series (2) 9 (1958), 114-131.

NAYAK, M.K., On the absolute Logarithmic summability L of Fourier integrals, Journal Indian Math. Soc. 34 (1970), 115-122.

RANGACHART, M.S., A generalization of Abel-type summability methods for functions, Indian J. Math. 7, No. 1 (1965), 17-23,

RANOACHARI, M.S., Correction to: A generalization of Abel-type summability methods for functions, Indian J. Math. 8, No. 2 (1966) 97.

WIDDER, D.V., The Laplace transform, Princeton, 1941.