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Zeriahi, Ahmed

Bases communes dans certains espaces de fonctions harmoniques et fonctions séparement harmoniques sur certains ensembles de \(C^ n\). (French) Zbl 0504.31002

Ann. Fac. Sci. Toulouse, V. Ser., Math. 4, 75-102 (1982).
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Cited in 2 Documents

MSC:

31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
32D10 Envelopes of holomorphy
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces

Keywords:

harmonic continuation; separately harmonic functions

Citations:

Zbl 0357.32002; Zbl 0265.46025; Zbl 0185.152
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Full Text: DOI Numdam EuDML

References:

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[2] Dudley, R.M. et Randol, B.. «Implications of point wise bounds on polynomials». Duke Math. J.29 (3), (1962), p. 455-458. · Zbl 0105.05004
[3] Jarnicki, M.. «Analytic continuation of harmonic functions». Zeszyty Nankowe UJ17, (1975), p. 93-104. · Zbl 0335.32009
[4] Le Long, P.. «Prolongement analytique et singularités complexes des fonctions harmoniques». Bull. Soc. Math. Belgique7 (1) (1954), p. 10-23. · Zbl 0068.08301
[5] Mityagin, B.S.. «Approximative dimension and bases in nuclear spaces». Russian Math. Surveys, t.16, (1961), p. 59-127. · Zbl 0104.08601
[6] Nguyen Thanh Van. «Bases de Schauder dans certains espaces de fonctions holomorphes». Ann. Inst. Fourier, t. 22 (1972), p. 169-253. · Zbl 0226.46025
[7] Nguyen Thanh Van. «Bases communes pour certains espaces de fonctions harmoniques». Bull. Sc. Math. 2e série, 97, (1973), p. 33-49. · Zbl 0265.46025
[8] Plesniak, W.. «Sur la L-régularité des compacts de Cn». Polycopié de la Fac. des Sciences de Toulouse, U.E.R. de Math., (1980).
[9] Sadullaev, A.. «P-regularity of sets in Cn. Proceeding of the conference on Analytic Functions Kozubnik 1979». n° 798, Springer-Verlag. · Zbl 0458.31005
[10] Siciak, J.. «Extremal plurisousharmonic functions in CN». Proceeding of the 1st Finish-Polish summer school in complex analysis Pod lesice, Lodz, (1977). · Zbl 0384.32005
[11] Siciak, J.. «Separetely analytic functions and enveloppes of holomorphy of some lower dimentional subsets of Cn». Ann. Pol. Math. t. 22, (1969), p. 145-171. · Zbl 0185.15202
[12] Siciak, J.. «Asymptotic behaviour of harmonic polynomials bounded on a compact set». Ann. Pol. Math. (1968), p. 267-278. · Zbl 0182.14702
[13] Zaharjuta, V.P.. «Fonctions plusisousharmoniques extrémales, échelles hilbertienne et isomorphisme d’espaces de fonctions analytiques de plusieurs variables complexes (en Russe)». Théorie des fonctions, Analyse fonctionnelle et leurs applications, t. 19 et 21, (1974), p. 133-157 et p. 65-83.
[14] Zaharjuta, V.P.. «Continuable bases in spaces of analytic functions of one and several variables». Siberian Math. J. t. 8, (1967), p. 204-216. · Zbl 0182.45302
[15] Zaharjuta, V.P.. «Separately analytic functions, generalisations of Hartog’s theorem and enveloppes of holomorphy». Mat. Sbornik, t. 101 (143), (1976), n° 1, p. 51-67. · Zbl 0381.32003
[16] Zeriahi, A.. «Sur les bases communes d’espaces de fonctions harmoniques et analytiques». Thèse de 3ème cycle, U.P.S. SciencesToulouse (1980).
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