Abstract
Some classes of spaces of generalized functions with special reference to the Laplace transformation are surveyed, the spaces being norm completions. It is proved using a theorem of G. D. Birkhoff that these spaces contain universal approximants.
Mathematics Subject Classification: primary 44A40, 44A10, secondary 44A35, 46F12.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. B. Miller, Generalized-function calculi for the Laplace transformation, Arch. for Rat. Mech. and Analysis, 12:409 (1963).
D.V. Widder, “The Laplace transform”, Princeton U. P., Princeton (1946).
J.B. Miller, Generalized Gâteaux and Fréchet derivatives in convolution algebras, Proc. Camb. Phil. Soc. 59:707 (1963).
J. B. Miller, Hilbert spaces of generalized functions extending L2, I and II, J. Austral. Math. Soc. 1: 281 (1960)
J. B. Miller, Hilbert spaces of generalized functions extending L2, I and II, J. Austral. Math. Soc. 3: 267 (1963)
J. B. Miller, On the solution of certain integral equations by generalized functions, Proc. Camb. Phil. Soc. 57:767(1961).
J. B. Miller, Normed spaces of generalized functions, Compositio Mathematica 15:127 (1963).
J. B. Miller, A class of series involving integral kernels, I and H. Math. Zeitsch. 76:257(1961)
J. B. Miller, A class of series involving integral kernels, I and H. Math. Zeitsch. 79:227(1962)
J. Mikusiński, “Operational Calculus”, Pergamon, New York (1959).
J. D. Weston, Positive perfect operators, Proc. London Math. Soc. 10:545 (1960).
J.B. Miller, Series like Taylor’s series, Aequationes Math. 26:208(1983).
E. T. Whittaker and G. N. Watson, “A course in modern analysis”, Camb. U. P., Cambridge (1946).
B. C. Berndt, Periodic Bernoulli numbers, summation formulae and applications, in: “Theory and application of special functions”, Academic Press, New York, 1975.
J. B. Miller, The standard summation operator, the Euler-Maclaurin sum formula, and the Laplace transformation, J. Austral. Math. Soc. (Series A) 39:367 (1985).
G. D. Birkhoff, Démonstration d’un théorème élémentaire sur les fonctions entiéres, Comptes rendus, Acad. des Sc. Paris 189: 473 (1929).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media New York
About this chapter
Cite this chapter
Miller, J.B. (1993). Generalized Functions for the Laplace Transform and Universal Approximants. In: Pathak, R.S. (eds) Generalized Functions and Their Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1591-7_12
Download citation
DOI: https://doi.org/10.1007/978-1-4899-1591-7_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-1593-1
Online ISBN: 978-1-4899-1591-7
eBook Packages: Springer Book Archive