Summary
We prove a generalization of the Rudin–Carleson theorem for homogeneous solutions of locally solvable real analytic vector fields.
2000 AMS Subject Classification: Primary: 35F15, 35B30, Secondary: 42A38, 30E25
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M. S. Baouendi and F. Treves, A property of the functions and distributions annihilated by a locally integrable system of complex vector fields, Ann. Math., 113 (1981), 387–421.
S. Berhanu, P. Cordaro, and J. Hounie, An introduction to involutive structures, Cambridge University Press, 2008.
S. Berhanu and J. Hounie, A Rudin–Carleson theorem for planar vector fields, Math. Annalen, to appear.
S. Berhanu and J. Hounie, An F. and M. Riesz theorem for planar vector fields, Math. Ann., 320 (2001), 463–485.
S. Berhanu and A. Meziani, Global properties of a class of planar vector fields of infinite type, Commun. Partial Differential Equations, 22 (1997), 99–142.
G. Bharali, On peak-interpolation manifolds for A(Ω) for convex domains in Cn, Trans. AMS, 356 (2004), 4811–4827.
E. Bishop, A general Rudin–Carleson theorem, Proc. AMS, 13 (1962), 140–143.
L. Carleson, Representations of continuous functions, Math. Z., 66 (1957), 447–451.
R. Doss, Elementary proof of the Rudin-Carleson and the F. and M. Riesz theorems, Proc. AMS, 82 (1981), 599–602.
H. Farkas and I. Kra, Riemann Surfaces, 2nd ed., Springer Verlag, 1991.
T. Gamelin, Uniform algebras, 2nd ed., Chelsea Pub. Co., 1984.
A. Nagel, Smooth zero sets and interpolation sets for some algebras of holomorphic functions on strictly pseudoconvex domains, Duke Math. J., 43 (1976), 323–348.
L. Nirenberg and F. Treves, Solvability of a first order linear partial differential equation, Commun. Pure Appl. Math., 16 (1963), 331–351.
D. Oberlin, A Rudin–Carleson theorem for uniformly convergent Taylor series, Michigan Math. J., 27 (1980), 309–313.
W. Rudin, Boundary values of continuous analytic functions, Proc. AMS, 7 (1956), 808–811.
W. Rudin, Peak-interpolation sets of class C 1, Pac. J. Math., 75 (1978), 267–279.
H. J. Sussmann, Orbits of families of vector fields and integrability of istributions, Trans. AMS, 180 (1973), 171–188.
F. Treves, Approximation and representation of functions and distributions annihilated by a system of complex vector fields, Centre Math. Ecole Polytechnique, Palaiseau, France, 1981.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Birkhäuser Boston
About this chapter
Cite this chapter
Berhanu, S., Hounie, J. (2009). A Generalization of the Rudin–Carleson Theorem. In: Bove, A., Del Santo, D., Murthy, M. (eds) Advances in Phase Space Analysis of Partial Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 78. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4861-9_3
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4861-9_3
Published:
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4860-2
Online ISBN: 978-0-8176-4861-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)