Projection method for the Hankel transform

Abstract

The numerical projection method for the zero-order Hankel transform inversion for the case of data given on a finite interval has been developed. The justification of the convergence of the projection method has been done for the general case that also includes the sine-Fourier transform inversion. An inequality on the norms of the zeroth-order Laguerre functions has been proved. The efficiency of the method was illustrated with the test data and for the problem of cylindrical distribution function calculation using the melt surface layer diffraction data.

Keywords:

• Hankel transform
• projection method
• Laguerre functions
• regularization theory

AMS Subject Classification :

• 42A38
• 65R10
• 65R32
• 42C10

Acknowledgements

The work was supported by the federal target programme ‘Scientific and scientific-pedagogical personnel of innovative Russia’ in 2009–2013 and RFBR grant 10-01-00535.