On a Class of Integral Equations Involving Kernels of Cosine and Sine Type
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.
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).
- [OzEtAl01]Ozaktas, H.M., Zalevsky, Z., Kutay, M.A.: The Fractional Fourier Transform with Applications in Optics and Signal Processing. Wiley, New York (2001)Google Scholar
- [PR01]Przeworska-Rolewicz, D.: Some open questions in algebraic analysis. In: Abe, J.M., Tanaka, S. (eds.) Unsolved Problems on Mathematics for the 21st Century, pp. 109–126, 1st edn. IOS Press, Amsterdam (2001)Google Scholar