Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616825 | Journal of Mathematical Analysis and Applications | 2013 | 11 Pages |
Abstract
Classical integral representation of the Mellin type kernel xâz=1Î(z)â«0âeâxttzâ1dt,x>0,Re z>0, in terms of the Laplace integral gives an idea to construct a class of non-convolution (index) transforms with the kernel kz±(x)=â«0âeâxt±1r(t)tzâ1dt,x>0, where r(t)â 0,tâR+ admits a power series expansion, which has an infinite radius of convergence and the integral converges absolutely in a half-plane of the complex plane z. Particular examples give the Kontorovich-Lebedev-like transformation and new transformations with hypergeometric functions as kernels. Mapping properties and inversion formulas are obtained. Finally we prove a new inversion theorem for the modified Kontorovich-Lebedev transform.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Semyon Yakubovich,