On exact solutions of Hankel equations

Petrov, V.

doi:10.1090/spmj/1534

On exact solutions of Hankel equations
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by V. E. Petrov
Translated by: A. Plotkin

St. Petersburg Math. J. 30 (2019), 123-148

DOI: https://doi.org/10.1090/spmj/1534

Published electronically: December 5, 2018

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Abstract:

For the Hankel operator on the semiaxis, new cases of explicit diagonalization are presented; the corresponding integral transformations and eigenfunctions of the continuous spectrum are found. The known cases of explicit diagonalization are also put into the framework of a unified approach. Also, the paper contains an extensive list of Hankel equations that reduce, in terms of the corresponding transformations, to various exactly solvable problems such as the Riemann problem, the Carleman problem, an ordinary differential equation, and so on.

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