The integral equations Au = f and u = Au + f are studied, where The kernel of A is non-integrable over  for any  The operator A is defined for all  except for a discrete set of values by analytic continuation. This is done using the Fourier transform. Sufficient conditions are found for the solution u to exist and to be smooth. Explicit formulas are given for such solutions.

hyper-singular integral equations.

Received: March 16, 2022; Accepted: April 7, 2022; Published: April 12, 2022

How to cite this article: Alexander G. Ramm, On hyper-singular multidimensional equations, Far East Journal of Theoretical and Applied Sciences 1 (2022), 1-4. http://dx.doi.org/10.17654/TAS2022001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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