Applications of the Kontorovich-Lebedev type Convolutions to Integral Equations
In this section we consider some class of second kind integral equations with the kernel (16.34), which contains the inner integral of the Kontorovich-Lebedev convolution (15.1). Such equations were mentioned in N.N. Lebedev (1949d) and their solutions were constructed using integral representations of the Macdonald function in the form (16.33). Later, in S.B. Yakubovich (1987 a,b), S.B. Yakubovich and A.I. Moshinskii (1993) the connection between these equations and the Kontorovich-Lebedev convolution (15.1) has been shown. In spite of the complication of the respective kernels for such type equations, as compared, for example, with the Fourier or Mellin convolution equations we could recognize their convolution structure due to the theory of the convolution (15.1).
KeywordsOperational Calculus Fourier Integral Convolution Equation Fubini Theorem Macdonald Function
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