...trengthening of this theorem is Fabry's gap theorem ([[Fabry theorem|Fabry theorem]]). If the lower density
...alued analytic function with simply-connected domain of existence (Pólya's theorem). See also [[Over-convergence|Over-convergence]].
1 KB (203 words) - 06:24, 22 April 2012
...defined near $K$. The complete answer is given by the [[Whitney extension theorem]].
3 KB (555 words) - 09:11, 12 December 2013
==Fabry's gap theorem==
...al boundary]]: all points of the cicle are singular points for $f(z)$. The theorem can be generalized to Dirichlet series.
2 KB (290 words) - 18:23, 10 October 2023
A deep theorem from the real analysis, showing which data are required to extent a real-va
'''Theorem''' (H. Whitney, 1934, {{Cite|W}}).
5 KB (913 words) - 12:24, 12 December 2020
...his form the Borel theorem is a particular case of the [[Whitney extension theorem]], see {{Cite|N}}.
This theorem is also referred to as the ''[[Borel-Ritt theorem]]'', see {{Cite|W|Sect. 9}}.
3 KB (454 words) - 09:11, 12 December 2013
$#C+1 = 30 : ~/encyclopedia/old_files/data/C020/C.0200870 Cauchy\ANDHadamard theorem
The content of the Cauchy–Hadamard theorem is thus expressed by the Cauchy–Hadamard formula (2), which should be und
4 KB (625 words) - 15:35, 4 June 2020
==Hadamard's gap theorem==
...gaps. See also [[Lacunary series|Lacunary series]]; [[Fabry theorem|Fabry theorem]].
10 KB (1,520 words) - 12:44, 21 April 2012
...is set and attains its least upper and greatest lower bounds (Weierstrass' theorem);
1 KB (204 words) - 16:14, 17 September 2017
$#C+1 = 13 : ~/encyclopedia/old_files/data/F038/F.0308260 Fatou theorem (on Lebesgue integrals)
A theorem on passing to the limit under a Lebesgue integral: If a sequence of measura
2 KB (343 words) - 19:38, 5 June 2020
...R><TR><TD valign="top">[a3]</TD> <TD valign="top"> H.S. Ruse, "Taylor's theorem in the tensor calculus" ''Proc. London Math. Soc.'' , '''32''' (1931) pp
4 KB (573 words) - 08:24, 6 June 2020
...i}}||valign="top"| A. Wiles, "Modular elliptic curves and Fermat's last theorem" ''Ann. of Math.'', '''141''' : 2–3 (1995) pp. 443–551 {{MR|133303
7 KB (1,047 words) - 01:52, 18 July 2022
In the general case the theorem on idempotent measures can be naturally interpreted in terms of the cohomol
4 KB (655 words) - 13:07, 7 April 2023
...35 : ~/encyclopedia/old_files/data/S110/S.1100160 Skolem\ANDMahler\ANDLech theorem
The theorem of Skolem–Mahler–Lech asserts that if a recurrence (equivalently, a gen
6 KB (908 words) - 06:04, 12 July 2022
...the algebra). The spectrum is a non-empty compact set (the Gel'fand–Mazur theorem). In the case of a commutative algebra, the spectrum coincides with the set
...valign="top">[2]</TD> <TD valign="top"> R. Harte, "The spectral mapping theorem in several variables" ''Bull. Amer. Math. Soc.'' , '''78''' (1972) pp. 8
3 KB (528 words) - 08:22, 6 June 2020
...al root numbers of a real representation is $+ 1$, so the Fröhlich–Queyrut theorem is a reciprocity law (cf. [[Reciprocity laws|Reciprocity laws]]), or a "pr
...e Galois extension of fields, with Galois group $G$. Then the normal basis theorem of field theory says that $N$ has a $K$-basis consisting of the Galois conj
12 KB (1,811 words) - 17:46, 1 July 2020
...ed most often in [[Universal algebra|universal algebra]], and in automatic theorem proving procedures.
Birkhoff's completeness theorem: If $S$ is an equational theory and $s = t$ is true in all the models of $S
9 KB (1,433 words) - 17:00, 1 July 2020
the theorem on the existence of a continuous solution of the problem (1)–(2) is appli
Taylor's formula may be used as the asymptotic formula for $ x ( t , \mu ) $
7 KB (968 words) - 17:33, 5 June 2020
...holomorphy if and only if it is holomorphically convex (the Cartan–Thullen theorem). A domain $ D $
...maps a domain of holomorphy onto a domain of holomorphy (the Behnke–Stein theorem).
6 KB (977 words) - 19:36, 5 June 2020
* the local inverse (in the case of the inverse function theorem)
...ing the equation $F(y, f(y))= F(x_0)$ (in the case of the inverse function theorem)
6 KB (1,048 words) - 21:19, 14 January 2021
...= 115 : ~/encyclopedia/old_files/data/P073/P.0703030 Poincar\Aee\ANDDulac theorem
The Poincaré theorem on canonical forms for formal differential equations says that if the eigen
11 KB (1,659 words) - 05:14, 24 February 2022