A representation theory for a general class of convolution transforms

A representation theory for a general class of convolution transforms
HTML articles powered by AMS MathViewer

Trans. Amer. Math. Soc. 67 (1949), 69-97

DOI: https://doi.org/10.1090/S0002-9947-1949-0032818-6

PDF | Request permission

References

Edwin J. Akutowicz, The third iterate of the Laplace transform, Duke Math. J. 15 (1948), 1093–1132. MR 27362

Lehrbuch der Funktionentheorie

R. P. Boas Jr., Asymptotic relations for derivatives, Duke Math. J. 3 (1937), no. 4, 637–646. MR 1546018, DOI 10.1215/S0012-7094-37-00352-1
R. P. Boas Jr., Inversion of a generalized Laplace integral, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 21–24. MR 5929, DOI 10.1073/pnas.28.1.21
R. P. Boas Jr. and D. V. Widder, The iterated Stieltjes transform, Trans. Amer. Math. Soc. 45 (1939), no. 1, 1–72. MR 1501983, DOI 10.1090/S0002-9947-1939-1501983-7
Harald Cramér, Mathematical Methods of Statistics, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J., 1946. MR 0016588
I. I. Hirschman Jr. and D. V. Widder, An inversion and representation theory for convolution transforms with totally positive kernels, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 152–156. MR 25617, DOI 10.1073/pnas.34.4.152
Harry Pollard, Note on the inversion of the Laplace integral, Duke Math. J. 6 (1940), 420–424. MR 1990
Harry Pollard, Integral transforms, Duke Math. J. 13 (1946), 307–330. MR 18264
Harry Pollard, The inversion of the transforms with reiterated Stieltjes kernels, Duke Math. J. 14 (1947), 129–142. MR 20661
Harry Pollard, The integral transforms with iterated Laplace kernels, Duke Math. J. 14 (1947), 659–674. MR 22627

Aufgaben und Lehrsätze aus der Analysis

I. J. Schoenberg, On totally positive functions, Laplace integrals and entire functions of the Laguerre-Polya-Schur type, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 11–17. MR 18706, DOI 10.1073/pnas.33.1.11
D. V. Widder, The inversion of the Laplace integral and the related moment problem, Trans. Amer. Math. Soc. 36 (1934), no. 1, 107–200. MR 1501737, DOI 10.1090/S0002-9947-1934-1501737-7

The Stieltjes transform

The Green’s function for a differential system of infinite order

The Laplace transform

D. V. Widder, Inversion formulas for convolution transforms, Duke Math. J. 14 (1947), 217–249. MR 21622, DOI 10.1215/S0012-7094-47-01417-8
D. V. Widder, The inversion of a generalized Laplace transform, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 295–297. MR 21623, DOI 10.1073/pnas.33.10.295