2012/09/09 by Semyon Yakubovich, Yakubovich, Semyon
Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Mathematical Analysis and Transform Methods #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1209.1799
Classical integral representation of the Mellin type kernel in terms of the\nLaplace integral gives an idea to construct a new class of non-convolution\n(index) transforms. Particular examples give the Kontorovich-Lebedev-like\ntransformation and new transformations with hypergeometric functions as\nkernels. Mapping properties and inversion formulas are obtained. Finally we\nprove a new inversion theorem for the modified Kontorovich-Lebedev transform\n