References
- Fourier , J . 1988 . Théorie Analytique de la Chaleur (French) , Paris : Reprint of the 1822 original, Jacques Gabay .
- Beck , JV , Blackwell , B and St. Clair , CR . 1985 . Inverse Heat Conduction: Ill-posed Problems , New York : John Wiley & Sons .
- Hào , DN . 1996 . “ Methods for Inverse Heat Conduction Problems ” . In Habilitationsschrift , Siegen : University of Siegen . Methoden und Verfahren der Mathematischen Physik (Methods and Procedures in Mathematical Physics), Vol. 43. Peter Lang, Frankfurt am Main, 1998
- Rooney , PG . 1957 . On the inversion of the Gauss transform . Canad. Math. Bull. , 9 : 459 – 464 .
- Rooney , PG . 1963 . A generalization of an inversion formula for the Gauss transformation . Canad. Math. Bull. , 6 : 45 – 53 .
- Saitoh , S . 1983 . The Weierstrass transform and an isometry in the heat equation . Appl. Anal. , 16 : 1 – 6 .
- Ulmer , W and Kaissl , W . 2003 . The inverse problem of a Gaussian convolution and its application to the finite size of measurement chambers/detectors in photon and proton dosimetry . Phys. Med. Biol. , 48 : 707 – 727 .
- Saitoh , S . 1997 . “ Integral Transforms, Reproducing Kernels and their Applications ” . In Pitman Research Notes in Mathematics Series , Vol. 369 , UK : Addison Wesley Longman .
- Saitoh , S , Hayashi , N and Yamamoto , M (eds) . 2001 . Analytic Extension Formulas and their Applications , Dordrecht : Kluwer Academic .
- Hirschman , II and Widder , DV . 1955 . The Convolution Transform , Princeton, NJ : Princeton University Press .
- Matsuura , T , Saitoh , S and Trong , DD . 2005 . Approximate and analytical inversion formulas in heat conduction on multidimensional spaces . J. Inverse Ill-posed Probl. , 13 : 479 – 493 .
- Matsuura , T and Saitoh , S . 2006 . Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley–Wiener spaces . Appl. Anal. , 85 : 901 – 915 .
- Saitoh , S . 2004 . Approximate real inversion formulae of the Gaussian convolution . Appl. Anal. , 83 : 727 – 733 .
- Tikhonov , AN and Arsenin , VI . 1977 . Solutions of Ill-posed Problems , New York : John Wiley & Sons .
- Castro , LP , Rojas , EM and Saitoh , S . Inversion from different kinds of information and real inversion formulas of the Laplace transform from a finite number of data . Mathematics in Engineering Science and Aerospace 1 , (to appear)
- Stenger , F . 1993 . “ Numerical Methods Based on Sinc and Analytic Functions ” . In Springer Series in Computational Mathematics , Vol. 20 , New York : Springer-Verlag .
- Iwamura , K , Matsuura , T and Saitoh , S . A numerical construction of a natural inverse of any matrix by using the theory of reproducing kernels with the Tikhonov regularization . Far East J. Math. Edu. , to appear
- Matsuura , T and Saitoh , S . 2005 . Dirichlet's principle using computers . Appl. Anal. , 84 : 989 – 1003 .
- Itou , H and Saitoh , S . 2007 . Analytical and numerical solutions of linear singular integral equations . Int. J. Appl. Math. Stat. , 12 : 76 – 89 .