A class of “central limit theorems” for convolution products of generalized functions
HTML articles powered by AMS MathViewer
- by Reuben Hersh
- Trans. Amer. Math. Soc. 140 (1969), 71-85
- DOI: https://doi.org/10.1090/S0002-9947-1969-0241971-3
- PDF | Request permission
References
- N. G. Bakhoom, Proc. London Math. Soc. (2) 35 (1933), 83.
- Felix Bernstein, Über das Fourierintegral $\smallint \limits _0^\infty e^{-x*}\cos txdx$, Math. Ann. 79 (1918), no. 3, 265–268 (German). MR 1511926, DOI 10.1007/BF01458208 W. R. Burwell, Proc. London Math. Soc. (2) 22 (1924), 57.
- William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
- I. M. Gel′fand and G. E. Šilov, Fourier transforms of rapidly increasing functions and questions of the uniqueness of the solution of Cauchy’s problem, Amer. Math. Soc. Transl. (2) 5 (1957), 221–274. MR 0083624, DOI 10.1090/trans2/005/05 G. H. Hardy and J. E. Littlewood, Ges. Wiss. Göttingen (1920), 33. L. Hörmander, Linear partial differential operators, Academic Press, New York, 1963. G. Pólya, J. Reine Angew. Math. 158 (1927), 6. G. N. Watson, A treatise on the theory of Bessel functions, Cambridge, 1962.
- Kôsaku Yosida, Functional analysis, Die Grundlehren der mathematischen Wissenschaften, Band 123, Academic Press, Inc., New York; Springer-Verlag, Berlin, 1965. MR 0180824
- Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, Vol. III, Interscience Publishers, a division of John Wiley & Sons, Inc., New York-London-Sydney, 1964. With special lectures by Lars Garding and A. N. Milgram. MR 0163043 A. I. Zhukov, Uspehi Mat. Nauk (3) 14 (1959), 129 V. Yu. Krylov, Dokl. Akad. Nauk SSSR. 139 (1961), 20 = Soviet Math. Dokl. 2 (1961), 855.
- V. Ju. Krylov, Some properties of the distribution corresponding to the equation $\partial u/\partial t=(-1)^{q+1} \partial ^{2q}u/\partial x^{2q}$, Soviet Math. Dokl. 1 (1960), 760–763. MR 0118953 Yu. P. Studnev, Teor. Verojatnost. i Primenen. 12 (1967), 668.
Bibliographic Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 140 (1969), 71-85
- MSC: Primary 46.40; Secondary 60.00
- DOI: https://doi.org/10.1090/S0002-9947-1969-0241971-3
- MathSciNet review: 0241971