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Applications of Analytic Continuation to Tables of Integral Transforms and Some Integral Equations with Hyper-Singular Kernels

DOI: 10.4236/ojop.2022.111001, PP. 1-6

Keywords: Analytic Continuation, Integral Equations with Hyper-Singular Kernels

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Abstract:

Analytic continuation of some classical formulas with respect to a parameter is discussed. Examples are presented. The validity of these formulas is greatly expanded. Application of these results to solving some integral equations with hyper-singular kernels is given.

 References

[1]  Bateman, H. and Erdelyi, A. (1954) Tables of Integral Transforms. Vol. 1, McGraw Hill, New York, USA.
[2]  Ramm, A.G. (2021) Navier-Stokes Equations Paradox. Reports on Mathematical Physics, 88, 41-45.
https://doi.org/10.1016/S0034-4877(21)00054-9
[3]  Ramm, A.G. (2021) The Navier-Stokes Problem. Morgan & Claypool Publishers, San Rafael, USA.
[4]  Ramm, A.G. (2021) Comments on the Navier-Stokes Problem. Axioms, 10, Article No. 95.
https://doi.org/10.3390/axioms10020095
[5]  Rudin, W. (1974) Real and Complex Analysis. McGraw Hill, New York, USA.

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