The Journal of Analysis

, Volume 27, Issue 1, pp 233–239 | Cite as

Certain remarks on functional equations of convolution types

  • P. DevarajEmail author
Original Research Paper


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.


Reconstruction Deconvolution Functional equations 

Mathematics Subject Classification

Primary 42A85 44A35; Secondary 42A75 39A12 


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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