On the Existence of Approximate Solution of Fredholm Integral Equation of the First Kind by Band-Limited Scaling Function

Original Research
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Abstract

In this paper, we study the existence and uniqueness of the solution of Fredholm integral equation of the first kind with convolution type kernel. These results are based on band-limited scaling function which is generated by a class of band-limited wavelets. Since these band-limited functions are infinitely differentiable and possess rapid decay property, methods based on these functions would be highly accurate. Finally, convergence analysis has been discussed to validate the approximate solution.

Keywords

Wavelets Multiresolution analysis Band-limited scaling function Integral equation Fourier transform 

Mathematics Subject Classification

45B05 45l05 65T60 

Notes

Acknowledgements

The first author would like to thank University Grants Commission for providing Ph. D. scholarship. Authors are grateful to the anonymous reviewers for their expert suggestions.

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsIndian Institute of Technology KanpurUttar PradeshIndia

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