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Certain remarks on functional equations of convolution types

Original Research Paper
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Abstract

We analyse the convolution equation of the type \(f\star \gamma =g,\) where \(f\star \gamma \) is the convolution of f and \(\gamma \) defined by \((f\star \gamma )(x)=\int _{{\mathbb{R}}}f(x-y)d\gamma (y),\) g is a given function and \(\gamma \) is a compactly supported Borel measure which is a sum of a compactly supported discrete Borel measure \(\mu \) and a compactly supported absolutely continuous measure \(\nu \) whose density function is a finite linear combination of indicator functions of intervals.

Keywords

Reconstruction Deconvolution Functional equations 

Mathematics Subject Classification

Primary 42A85 44A35; Secondary 42A75 39A12 

Notes

Compliance with ethical standards

Conflict of interest

There is no conflict of interest and no funding has been received for the work.

Research involving human participants and/or animals

This research does not involve neither human nor animals participants.

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Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.School of MathematicsIndian Institute of Science Education and ResearchThiruvananthapuramIndia

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