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Integral transforms

Handbooks

The transforms and applications handbook, ed Poularikas A D (CRC, 2000)

Schiff J L, Laplace transformation: theory and applications (Springer,1999)

Prudnikov A P, Brychkov Y A, Marichev O I, Direct Laplace transforms (Gordon and Breach, 1992)

Диткин В А, Прудников А П, Интегральные преобразования и операционное исчисление (Наука, 1974)

Деч Г, Руководство к практическому применению преобразования Лапласа и z-преобразования (Наука, 1971)

Бейтмен Г, Эрдейи А, Таблицы интегральных преобразований (Наука, 1969, 1970)

Inversion of Laplace transforms

Abate J, Choudhury G L, Whitt W, An introduction to numerical transform inversion and its application to probability models, in Computational Probability, ed Grassman W, 257 (Kluwer, 1999)

Eaton D F, Recommended methods for fluorescence decay analysis, Pure Appl Chem 62, 1631 (1990)


Kryzhniy V V, High-resolution exponential analysis via regularized numerical inversion of Laplace transforms, J Comput Phys 199, 618 (2004)

Wagner U, Geyer A L J, A maximum entropy method for inverting Laplace transforms of probability density functions, Biometrika 82, 887 (1995)

Essah W A, Delves L M, On the numerical inversion of the Laplace transform, Inverse Problems 4, 705 (1988)

Bertero M, Brianzi P, Pike E R, On the recovery and resolution of exponential relaxation rates from experimental data. III. The effect of sampling and truncation of data on the Laplace transform inversion, Proc R Soc A 398, 23 (1985)

Bertero M, Boccacci P, Pike E R, On the recovery and resolution of exponential relaxation rates from experimental data. II. The optimum choice of experimental sampling points for Laplace transform inversion, Proc R Soc A 393, 51 (1984)

Bertero M, Boccacci P, Pike E R, On the recovery and resolution of exponential relaxation rates from experimental data: A singular value analysis of the Laplace transform inversion in the presence of noise, Proc R Soc A 383, 15 (1982)