Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique
Annales Polonici Mathematici (1996)
- Volume: 63, Issue: 1, page 35-50
- ISSN: 0066-2216
Access Full Article
topAbstract
topHow to cite
topA. Zeriahi. "Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique." Annales Polonici Mathematici 63.1 (1996): 35-50. <http://eudml.org/doc/262537>.
@article{A1996,
author = {A. Zeriahi},
journal = {Annales Polonici Mathematici},
keywords = {Green function; L² estimation; approximation; growth; extension; best polynomial approximation; holomorphic functions; algebraic manifold; entire function; convergence},
language = {fre},
number = {1},
pages = {35-50},
title = {Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique},
url = {http://eudml.org/doc/262537},
volume = {63},
year = {1996},
}
TY - JOUR
AU - A. Zeriahi
TI - Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique
JO - Annales Polonici Mathematici
PY - 1996
VL - 63
IS - 1
SP - 35
EP - 50
LA - fre
KW - Green function; L² estimation; approximation; growth; extension; best polynomial approximation; holomorphic functions; algebraic manifold; entire function; convergence
UR - http://eudml.org/doc/262537
ER -
References
top- [B-T] E. Bedford and B. A. Taylor, Plurisubharmonic functions with logarithmic singularities, Ann. Inst. Fourier (Grenoble) 38 (4) (1988), 133-171. Zbl0626.32022
- [Be] S. Bernstein, Sur l'ordre de la meilleure approximation polynomiale des fonctions continues, Bruxelles, 1912.
- [Bj] J.-E. Björk, On extensions of holomorphic functions satisfying a polynomial growth condition on algebraic varieties in , Ann. Inst. Fourier (Grenoble) 24 (4) (1974), 157-165. Zbl0288.32014
- [De] J.-P. Demailly, Mesures de Monge-Ampère et caractérisation géométrique des variétés algébriques affines, Mém. Soc. Math. France 19 (1985). Zbl0579.32012
- [D-M] P. B. Djakov and B. S. Mityagin, The structure of polynomial ideals in the algebra of entire functions, preprint of the Institute of Mathematics, Polish Academy of Sciences, no. 123, 1977.
- [H] L. Hörmander, An Introduction to Complex Analysis in Several Variables, Van Nostrand, Princeton, 1973. Zbl0271.32001
- [L-G] P. Lelong and L. Gruman, Entire Functions of Several Variables, Springer, 1986. Zbl0583.32001
- [Ng] T. V. Nguyen, Croissance et meilleure approximation polynomiale des fonctions entières, Ann. Polon. Math. 24 (1972), 325-333. Zbl0241.30043
- [No] K. J. Nowak, The extension of holomorphic functions of polynomial growth on algebraic sets in , Osnabrücker Schriften zur Math., 1984.
- [R,1] L. L. Ronkin, Continuation with estimates of holomorphic functions on sets of zeros of polynomials, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 128, 36 (1981), 89-103.
- [R,2] L. L. Ronkin, Entire functions, in: Encyclopedia of Math. Sci., Several Complex Variables III, Springer, 1986, 1-30.
- [R-W] K. Rusek and T. Winiarski, Criteria for regularity of holomorphic mappings, Bull. Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), 471-475. Zbl0507.14003
- [Sa] A. Sadullaev, An estimate for polynomials on analytic sets, Math. USSR-Izv. 20 (1980), 493-502. Zbl0582.32023
- [Si,1] J. Siciak, On some extermal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc. 105 (1962), 322-357. Zbl0111.08102
- [Si,2] J. Siciak, Extremal plurisubharmonic functions in , Ann. Polon. Math. 39 (1981), 175-211. Zbl0477.32018
- [Si,3] J. Siciak, Approximation by transcendental polynomials, Ann. Polon. Math. 46 (1985), 299-309. Zbl0604.32013
- [Sk] H. Skoda, Morphismes surjectifs et fibrés linéaires semi-positifs, dans : Séminaire P. Lelong-H. Skoda (Analyse), Lecture Notes in Math. 694, Springer, 1978.
- [Wa] J. Walsh, Interpolation and Approximation by Rational Functions, Boston, 1960.
- [Wi,1] T. Winiarski, Approximation and interpolation of entire functions, Ann. Polon. Math. 23 (1970), 259-273. Zbl0205.37905
- [Wi,2] T. Winiarski, Application of approximation and interpolation methods to the examination of entire functions of n variables, Ann. Polon. Math. 28 (1973), 98-121. Zbl0257.32008
- [Za] V. P. Zakharyuta, Extremal plurisubharmonic functions, orthogonal polynomials and the Bernstein-Walsh theorem for analytic functions of several complex variables, Ann. Polon. Math. 33 (1976), 137-148 (in Russian).
- [Ze,1] A. Zeriahi, Meilleure approximation polynomiale et croissance des fonctions holomorphes sur une variété algébrique affine, Ann. Inst. Fourier (Grenoble) 37 (2) (1987), 79-104. Zbl0596.32025
- [Ze,2] A. Zeriahi, Fonction de Green pluricomplexe à pôle à l'infini sur un espace de Stein parabolique et applications, Math. Scand. 69 (1991), 89-126.
- [Ze,3] A. Zeriahi, Ensembles pluripolaires exceptionnels pour la croissance partielle des fonctions holomorphes, Ann. Polon. Math. 50 (1989), 81-91. Zbl0688.32004
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.