# On a Class of Integral Equations Involving Kernels of Cosine and Sine Type

## Abstract

We consider a class of integral equations characterized by kernels of cosine and sine type and study their solvability. Moreover, we analyse the integral operator *T*, which is generating those equations, by identifying its characteristic polynomial, characterizing its invertibility, spectrum, Parseval-type identity and involution properties. Additionally, a new convolution is here introduced, associated with *T*, for which we deduce a corresponding factorization property.

## Notes

### Acknowledgements

This work was supported in part by Portuguese funds through the CIDMA – *Center for Research and Development in Mathematics and Applications*, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e a Tecnologia”), within project UID/MAT/04106/2013. The second named author was also supported by FCT through the Ph.D. scholarship PD/BD/114187/2016. The third named author was supported partially by the Viet Nam National Foundation for Science and Technology Developments (NAFOSTED).

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