A Banach algebra of functions with bounded 𝑛th differences

Daly, John T.; Downum, Philip B.

doi:10.1090/S0002-9947-1976-0425616-9

A Banach algebra of functions with bounded $n$th differences
HTML articles powered by AMS MathViewer

by John T. Daly and Philip B. Downum

Trans. Amer. Math. Soc. 223 (1976), 279-294

DOI: https://doi.org/10.1090/S0002-9947-1976-0425616-9

PDF | Request permission

Abstract:

Several characterizations are given for the Banach algebra of $(n - 1)$-times continuously differentiable functions whose $(n - 1)$st derivative satisfies a bounded Lipschitz condition. The structure of the closed primary ideals is investigated and spectral synthesis is shown to be satisfied.

References

R. P. Boas Jr. and D. V. Widder, Functions with positive differences, Duke Math. J. 7 (1940), 496–503. MR 3436
Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1963. MR 0157156
Georges Glaeser, Synthèse spectrale des idéaux de fonctions lipschitziennes, C. R. Acad. Sci. Paris 260 (1965), 1539–1542 (French). MR 173952
Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
A. Wayne Roberts and Dale E. Varberg, Convex functions, Pure and Applied Mathematics, Vol. 57, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973. MR 0442824
Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0210528
Donald R. Sherbert, The structure of ideals and point derivations in Banach algebras of Lipschitz functions, Trans. Amer. Math. Soc. 111 (1964), 240–272. MR 161177, DOI 10.1090/S0002-9947-1964-0161177-1
Lucien Waelbroeck, Closed ideals of Lipschitz functions, Function Algebras (Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965) Scott-Foresman, Chicago, Ill., 1966, pp. 322–325. MR 0194926