“Ilm-fan muammolari yosh tadqiqotchilar talqinida”
mavzusidagi 9-sonli respublika ilmiy konferensiyasi
118
2-teorema.
Faraz qilaylik,
0
0
0
(
)
(
)
m
m
f z
c
z
=
=
bir jinsli qator
n
E
Ј
to‘plamning har bir
0
z
E
nuqtasida yaqinlashuvchi bo‘lsin. U holda (1) darajali
qator quyidagi
(
)
*
: exp
,
1
n
G
z
z E
=
Ј
(4)
ochiq to‘plam ichida tekis yaqinlashadi, bu yerda
(
)
*
,
z E
–
E
to‘plamdagi
Roben funksiyasi,
( )
1
0,
exp
G
B
E
va
G
– psevdoqavariq soha.
Foydalanilgan adabiyotlar:
1.
Bedford E., Taylor B.A., A new capacity for plurisubharmonic functions,
Acta Math., V.149, 1982, pp. 1–40.
2.
Bloom T., Levenberg N. and Ma’u S., Robin functions and extremal
functions. Annales Polonici Mathematici, 80, (2003), pp. 55-84.
3.
Forelli F., Plurisubharmonicity in terms of harmonic slices, Math.
Scand., V. 41, 1977, 358-364.
4.
Sadullaev A., Plurisubharmonic functions, In Several complex variables
II. Berlin: Springer, Q3 1994. pp. 59–106. (Encyclopaedia of Mathematical Sciences;
vol. 8).
5.
Sadullaev A., Holomorphic continuation of a formal series along analytic
curves, Complex Variables and Elliptic Equations, Published on: 22 Sep 2020, pp. 1-
10.
6.
Sadullaev A., A class of maximal plurisubharmonic functions, Annales
Polonici Mathematici. 106, (2012), pp. 265-274.
7.
Sadullaev A., On Maximal Plurisubharmonic Functions, CRM
Proceedings and Lecture Notes., Canada, 55, (2012), pp. 211-216.
8.
Siciak J., A characterization of analytic functions of
n
variables, Studia
Mathematica, 35 (1970), pp. 293-297.
9.
Siciak J., On series of homogeneous polynomials and their partial sums,
Ann. Pol. Math. 51 (1990), pp. 289-302.
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