A self-contained approach to Mellin transform analysis for square integrable functions; applications

Integral Transforms and Special Functions

Volumn 8, Issue 3-4, 1999, Pages 175-198

  Butzer, Paul L ^a   Jansche, Stefan ^b  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b UNIVERSITY OF KIEL   (Germany)

Author keywords

Exponential sampling; Finite Mellin transforms; Mellin transforms for square integrable functions; Mellin translation and convolution; Mellin Fourier series; Mellin Kramer sampling theory

Indexed keywords

EID: 0343058144     PISSN: 10652469     EISSN: None     Source Type: Journal    
DOI: 10.1080/10652469908819226     Document Type: Article

References (21)

1. M. Bertero, Sampling theory, resolution limits and inversion methods, In Inverse Problems in Scattering and Imaging, (M. Bertero and E.R. Pike, Editors), Malvern Physics Series, Adam Hilger, Bristol, 1992, 71-94.
2. M. Bertero and E.R. Pike, Exponential sampling method for Laplace and other dilationally invariant transforms. I. Singular-system analysis, II. Examples in photon correction spectroscopy and Frauenhofer diffraction, Inverse Problems 7 (1991), 1-20, 21-41.
3. P.L. Butzer, M. Hauss, and R.-L. Stens, The sampling theorem and its unique role in various branches of mathematics, Mitt. Math. Ges. Hamburg 12 (1991), 523-547.
4. P.L. Butzer and S. Jansche, A direct approach to the Mellin transform, J. Fourier Anal. Appl. 3 (1997), 325-376.
5. P.L. Butzer and S. Jansche, The finite Mellin transform, Mellin-Fourier series, and the Mellin-Poisson summation formula, Proc. 3rd Int. Conference on Functional Analysis and Approximation Theory, Maratea, Sept. 1996 (ed. by F. Altomare et al). In Supplemento ai Rendiconti del Circolo Matematico di Palermo, 52 (1998), 55-81.
6. P.L. Butzer and S. Jansche, Mellin transform theory and the role of its differential and integral operators, In Proceedings of the Workshop on Transform Methods and Special Functions, Varna, August 1996 (P. Rusev, I. Dimovski and V. Kiryakova, Editors), Inst. of Math, and Informatics, Bulg. Acad. Sci., Sofia 1998.
7. P.L. Butzer and S. Jansche, The exponential sampling theorem of signal analysis, Atti. Sem. Fis. Univ. Modena, XLVI (1998), 99-122.
8. P.L. Butzer and S. Jansche, Mellin-Fourier series and classical Mellin transform, Proc. Conf. on Approximation in Mathematics, Memphis, March 1997 (G. Anastassiou, Editor), In Computers and Mathematics with Applications, (to appear 1999).
9. P.L. Butzer and G. Nasri-Roudsari, Kramer's sampling theorem in signal analysis and its role in mathematics, In Mathematical Methods and Applications, (J.M. Blackedge, Editor), Proc. Conf. on Image Processing, Cranfield Univ., September 1994, The Institute of Mathematics and its Applications, New Series Number 61, Clarendon Press, Oxford, 1997, 49-95.
10. P.L. Butzer, W. Splettstößer, and R.L. Stens, The sampling theorem and linear prediction in signal analysis, Jahresber. Deutsch. Math.-Verein. 90 (1988), 1-70.
11. P.L. Butzer and R.L. Stens, An extension of Kramer's sampling theorem for not necessarily "bandlimited" signals - the aliasing error, Acta Sci. Math. (Szeged) 60 (1995), 59-69.
12. D. Casasent (Editor), Optical Data Processing, Springer, Berlin 1978, 241-282.
13. F. Gori, Sampling in optics, In Advanced Topics in Shannon Sampling and Interpolation Theory, (R.J. Marks II, Editor), Springer, New York, 1993, 37-83.
14. E. Hewitt and K. Stromberg, Real and Abstract Analysis, Graduate Texts in Math. 25, Springer, New York, 1965.
15. J.R. Higgins, Sampling Theory in Fourier and Signal Analysis, Foundations, Clarendon Press, Oxford, 1996.
16. D. Naylor, On a Mellin type integral transform, J. Math. Mechs. 12 (1963), 265-274.
17. N. Ostrowsky, D. Sornette, P. Parker and E.R. Pike, Exponential sampling method for light scattering polydisperity analysis, Opt. Acta 28 (1981), 1059-1070.
18. I.N. Sneddon, The Use of Integral Transforms, McGraw-Hill, New York, 1972.
19. J. Tweed, Some dual integral equations involving inverse finite Mellin transforms, Glasgow Math. J. 14 (1973), 179-184.
20. A.I. Zayed, Advances in Shannon's Sampling Theory, CRC Press, Boca Raton, 1993.
21. A.I. Zayed, Handbook of Function and Generalized Function Transformations, CRC Press, Boca Raton, 1996.