A class of integral transforms related to the Fourier cosine convolution. (English) Zbl 1085.42003
Summary: “The class of integral transforms related to the Fourier cosine convolution is studied on \(L_{2}(R_{+})\). A Watson’s type theorem is proved. The concept of the symmetric Fourier cosine kernel with a characteristic polynomial \(r_n(x)= \Sigma^n_{m=0}a_mx^{2m}\) is defined. Plancherel’s theorem is formulated. The integral transforms with unsymmetric kernels are studied. Examples of certain kernels and transforms are given”.
Reviewer: H.-J. Glaeske (Jena)
MSC:
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 44A05 | General integral transforms |
| 44A35 | Convolution as an integral transform |
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