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991.
Manabu Naito 《Monatshefte für Mathematik》2002,136(3):237-242
This paper is concerned with the problem of counting the number of zeros of bounded nonoscillatory solutions of higher-order
linear ordinary differential equations involving a parameter. It is shown that a recent result for the second-order case is
still valid for the higher-order case.
Received September 20, 2001; in revised form February 8, 2002 Published online July 12, 2002 相似文献
992.
Clemens Heuberger 《Monatshefte für Mathematik》2001,132(4):325-339
In a recent paper [7] the author considered the family of parametrized Thue equations
for monic polynomials which satisfy
Under some technical conditions it could be proved that there is a computable constant such that for all integers the only integer solutions of the Diophantine equation satisfy .
In this paper, we give an explicit expression for depending on the polynomials .
(Received 5 September 2000; in revised form 30 December 2000) 相似文献
993.
Theω′-topology on the spaceL(X, Y) of bounded linear operators from the Banach spaceX into the Banach spaceY is discussed in [10]. Let ℒw' (X, Y) denote the space of allT∈L(X, Y) for which there exists a sequence of compact linear operators (T
n)⊂K(X, Y) such thatT=ω′−limnTn and let
. We show that
is a Banach ideal of operators and that the continuous dual spaceK(X, Y)* is complemented in
. This results in necessary and sufficient conditions forK(X, Y) to be reflexive, whereby the spacesX andY need not satisfy the approximation property. Similar results follow whenX andY are locally convex spaces.
Financial support from the Potchefstroom University and Maseno University is greatly acknowledged.
Financial support from the NRF and Potchefstroom University is greatly acknowledged. 相似文献
994.
Annunziata Esposito 《Rendiconti del Circolo Matematico di Palermo》2004,53(3):437-442
Let u be harmonic in a simply connected domainG ⊂ ℝ2 and letK be a compact subset of G. In this note, it is proved there exists an “elliptic continuation” of u, namely there exist a smooth
functionu
1 and a second order uniformly elliptic operatorL with smooth coefficients in ℝ2, satisfying:u
1=u inK, Lu
1=0 in ℝ2. A similar continuation theorem, with u itself a solution to an elliptic second order equation inG, is also proved. 相似文献
995.
H.?NaritaEmail author 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2004,74(1):253-279
For holomorphic modular forms on tube domains, there are two types of known Fourier expansions, i.e. the classical Fourier
expansion and the Fourier-Jacobi expansion. Either of them is along a maximal parabolic subgroup. In this paper, we discuss
Fourier expansion of holomorphic modular forms on tube domains of classical type along the minimal parabolic subgroup. We
also relate our Fourier expansion to the two known ones in terms of Fourier coefficients and theta series appearing in these
expansions. 相似文献
996.
C.?ElsnerEmail author 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2004,74(1):33-48
The paper introduces an algorithm which transforms homogeneous algebraic differential equations into universal differential
equations (in the sense of L. A. Rubel) havingC
n
(ℝ)-solutions. By applications of the algorithm to different initial equations some new universal differential equations
are found, and all the known equations due to R. J. Duffin are rediscovered with this method. Assuming weak conditions one
can find Cn(ℝ)-solutionsy of the differential equation
close to any continuous function such that 1,
with 0 ≤k
1 <k
2 < .... <k
s
≤n are linearly independent over the field of real algebraic numbers at the rational points q1,...,qs. 相似文献
997.
998.
We deal with compact Kähler manifolds M acted on by a compact Lie group K of isometries, whose complexification K has exactly one open and one closed orbit in M. If the K-action is Hamiltonian, we investigate topological and cohomological properties of M. 相似文献
999.
Bernhard Lamel 《Monatshefte für Mathematik》2004,142(4):315-326
We prove the following regularity result: If
,
are smooth generic submanifolds and M is minimal, then every Ck-CR-map from M into M which is k-nondegenerate is smooth. As an application, every CR diffeomorphism of k-nondegenerate minimal submanifolds in
of class Ck is smooth. 相似文献
1000.
Erhard Aichinger 《Monatshefte für Mathematik》2004,143(2):89-103
We show that the variety of near-rings and the variety of zero-symmetric near-rings are both generated by their finite members. We show this in a more general context: if a variety
is generated by a class of algebras
, then the variety of
-composition algebras is generated by the class of all full function algebras on direct products of finitely many copies of algebras in
. 相似文献