Point derivations of function algebras generated by holomorphic functions
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- by R. G. M. Brummelhuis and P. J. de Paepe PDF
- Proc. Amer. Math. Soc. 105 (1989), 117-120 Request permission
Abstract:
It is shown that a continuous point derivation on the algebra $H(X)$ consisting of uniform limits on $X$ of functions holomorphic in a neighborhood of a compact subset $X$ in ${{\mathbf {C}}^n}$, which vanishes on the polynomials is the trivial derivation.References
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R. G. M. Brummelhuis and P. J. de Paepe, Derivations on algebras of holomorphic functions, Department of Math., Univ. of Amsterdam, Preprint Series 87-23, 1987 .
- T. W. Gamelin, Embedding Riemann surfaces in maximal ideal spaces, J. Functional Analysis 2 (1968), 123–146. MR 0223894, DOI 10.1016/0022-1236(68)90014-1
- Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
- Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696 L. Hörmander, An introduction to complex analysis in several variables, North-Holland, 1973.
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 117-120
- MSC: Primary 46J15
- DOI: https://doi.org/10.1090/S0002-9939-1989-0933512-8
- MathSciNet review: 933512