A class of integral transforms related to the fourier cosine convolution

Abstract

In this work the class of integral transforms related to the Fourier cosine convolution is studied on L ₂(R ₊). Watson’s type theorem is proved. The concept of the symmetric Fourier cosine kernel with a characteristic polynomial is defined. Plancherel’s theorem is formulated. The integral transforms with unsymmetric kernels are studied. Examples of certain kernels and transforms are given.

Keywords:

• Fourier cosine transform
• Convolution
• Plancherel theory
• Watson theorem