Supported by NATO Grant No. RG 073.81.
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
L. Ahlfors and M. Heins, Questions of regularity connected with the Phragmén-Lindelöf principle, Ann. of Math., (2) 50 (1949), 341–346.
G. R. Allan, Ideals of rapidly growing functions, Proceedings International Symposium on Functional Analysis and its Applications, Ibadan, Nigeria, 1977.
W. G. Bade, Multipliers of weighted l 1 algebras, this Volume.
W. G. Bade and H. G. Dales, Norms and ideals in radical convolution algebras, J. Functional Analysis, 41 (1981), 77–109.
R. P. Boas, Jr., Entire Functions, Academic Press, New York, 1954.
F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, New York, 1973.
L. de Branges, Hilbert Spaces of Entire Functions, Prentice Hall, New Jersey, 1968.
T. Carleman, L'Integrale de Fourier et Questions Qui s'y Rattachent, Almquist and Wiksells, Uppsala, 1944.
M. L. Cartwright, On functions which are regular and of finite order in an angle, Proc. London Math. Soc., (2) 38 (1935), 158–179.
H. G. Dales, Automatic continuity: a survey, Bull. London Math. Soc., 10 (1978), 129–183.
H. G. Dales and W. K. Hayman, Esterle's proof of the Tauberian theorem for Beurling algebras, Ann. Inst. Fourier, Grenoble, 31 (1981), 141–150.
Y. Domar, A solution of the translation-invariant subspace problem for weighted Lp on R, R + or Z, this Volume.
_____, Bilaterally translation-invariant subspaces of weighted Lp(R), this Volume.
J. Esterle, Homomorphismes discontinus des algèbres de Banach commutatives separables, Studia Math., 66 (1979), 119–141.
_____, Universal properties of some commutative radical Banach algebras, J. Reine Angew. Math., 321 (1981), 1–24.
_____, A complex-variable proof of the Wiener Tauberian theorem, Ann. Inst. Fourier, Grenoble, 30 (1980), 91–96.
_____, Elements for a classification of commutative radical Banach algebras, this Volume.
I. M. Gelfand, D. A. Raikov, and G. E. Å ilov, Commutative Normed Rings, Chelsea, New York, 1964.
F. Ghahramani, Homomorphisms and derivations on weighted convolution algebras, J. London Math. Soc., (2) 21 (1980), 149–161.
J. I. Ginsberg and D. J. Newman, Generators of certain radical algebras, J. Approximation Theory, 3 (1970), 229–235.
S. Grabiner, Derivations and automorphisms of Banach algebras of power series, Mem. Amer. Math. Soc., 146 (1974).
V. P. Gurarii, Harmonic analysis in spaces with a weight, Trans. Moscow Math. Soc., 35 (1979), 21–75.
W. K. Hayman, Questions of regularity connected with the Phragmén-Lindelöf principle, J. Math. Pures et Appliquées, 35 (1956), 115–126.
W. K. Hayman and B. Korenblum, An extension of the Riesz-Herglotz formula, Annales Academiae Scientiarum Fennicae, Series A1, Mathematica, 2 (1976), 175–201.
E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Colloquium Publications Series, Vol. 31, Amer. Math. Soc., Providence, Rhode Island, 1957.
N. P. Jewell and A. M. Sinclair, Epimorphisms and derivations on L1[0,1] are continuous, Bull. London Math. Soc., 8 (1976), 135–139.
G. K. Kalisch, A functional analysis proof of Titchmarsh's theorem on convolution, J. Math. Anal. and Appl., 5 (1962), 176–183.
Y. Katznelson, An Introduction to Harmonic Analysis, Dover, New York, 1976.
B. Korenblum and K. Samotij, in preparation.
M. G. Krein, A contribution to the theory of entire functions of exponential type, Izvestiya Akad. Nauk SSSR, 11 (1947), 309–326 (Russian).
L. H. Loomis, An Introduction to Abstract Harmonic Analysis, van Nostrand, New Jersey, 1953.
J. Mikusiński, Operational Calculus, Pergamon Press, Oxford, 1959.
B. Nyman, On the one-dimensional translation group and semi-group in certain function spaces, Uppsala Thesis, 1950.
R. E. A. C. Paley and N. Wiener, Fourier Transforms in the Complex Domain, Colloquium Publications Series, Vol. 19, Amer. Math. Soc., New York, 1934.
J. R. Ringrose, Compact Non-Self-Adjoint Operators, van Nostrand-Reinhold, New York, 1971.
W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966.
L. Schwartz, Étude des Sommes d'exponentielles Réelles, Hermann, Paris, 1943.
A. M. Sinclair, Continuous Semigroups in Banach Algebras, London Mathematical Lecture Note Series, 63, Cambridge University Press, 1982.
P. Szász, Uber die Approximation stetiger Funktionen durch lineare Aggregate von Potenzen, Math. Ann., 77 (1916), 482–496.
E. C. Titchmarsh, The Theory of Functions, Oxford University Press, Oxford, 1939 (2nd edition).
D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, 1941.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Dales, H.G. (1983). Convolution algebras on the real line. In: Bachar, J.M., Bade, W.G., Curtis, P.C., Dales, H.G., Thomas, M.P. (eds) Radical Banach Algebras and Automatic Continuity. Lecture Notes in Mathematics, vol 975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064550
Download citation
DOI: https://doi.org/10.1007/BFb0064550
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11985-2
Online ISBN: 978-3-540-39454-9
eBook Packages: Springer Book Archive