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1.
The paper improves and generalizes a classical result from Paley and Wiener in their book on Fourier transforms. Paley and Wiener gave conditions on functionsh
n
that imply that the sequence (1+h
n
(x))e
inx
is a Riesz basis forL
2[–,]. These conditions involve theL
2-norm of the second derivativesh
n
. The new results replace the differential operatoryy by more general differential operators inL
2-spaces, in particular, by the Hermite differential operator inL
2(R), ande
inx
by arbitrary orthonormal bases. 相似文献
2.
Andrea Laforgia Martin E. Muldoon 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1988,39(2):267-271
Summary We show, among other things, that the positive zeros of a solution ofy
+x
y=0,y(0)=0 decrease to 1 as increases, 0.
To the memory of Milo Háik
This research was supported by grants from the Natural Sciences and Engineering Research Council (Canada) and Consiglio Nazionale delle Ricerche (Italy). Some of the work was done while the second-named author was visiting the Department of Mathematics, University of Torino. 相似文献
Sommario Si dimostra, tra l'altro, che gli zeri positivi d'una soiuzione diy +x y=0,y(0)=0 decrescono al limite 1, quando cresce, 0.
To the memory of Milo Háik
This research was supported by grants from the Natural Sciences and Engineering Research Council (Canada) and Consiglio Nazionale delle Ricerche (Italy). Some of the work was done while the second-named author was visiting the Department of Mathematics, University of Torino. 相似文献
3.
Hans -Jörg Reiffen 《manuscripta mathematica》1970,3(3):271-287
In this paper we study residue class rings in the sequel called algebras - where R is the ring of germs of complex-valued C- resp. C-functions at the origin of IRN and is an ideal with. If we have R=R(N) and with an ideal of germs of holomorphic functions, then we call A holomorphic. For holomorphic algebras it is possible to introduce the modules (A),p,q(A) of differential forms of degree r and of bidegree (p,q) in a natural way. We have. An almost holomorphic (almost complex) structure on an algebra A is a direct sum 1(A)=+ with the following property: for the projections p:1', p:1 we have
for all 1. Holomorphic algebras have an almost holomorphic structure. We collect some elementary properties of almost holomorphic algebras and then we prove a criterion for integrability in the analytic case, using Cartan's theory of germs of real-analytic sets. 相似文献
4.
, (n), - (P
n
), P
n
(A
n
)>0P
n
(A
n
)0,n. [15] - , . , P
n
P
n
T
n
T
n
. 相似文献
5.
M. van Veldhuizen 《Numerische Mathematik》1978,30(3):267-279
Summary A finite element method using piecewise polynomials of degree k is used to approximate the problem u+u=f, >0 a small parameter. A very irregular mesh is used. On this mesh error estimates of order0(h
k+1) are obtained uniformly in ,h the maximum stepsize, fork2. The condition number of the system of linear equations one has to solve in order to get the approximation is estimated. Extension of the results to more complicated problems is briefly indicated. Finally, a numerical example is given.Work performed while visiting the IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y. 相似文献
6.
Deng Shitao 《数学学报(英文版)》1989,5(3):223-234
ForH C
2 (,R) where 0 R
2n
,H (0)=0 and detH(0)0, the paper proves that there is a global Hopf bifurcation fromx=0 for Hamiltonian systemx=JH(x) iffJH(0)possesses purely imaginary eigenvalues. The work improves the corresponding result of J.C.Alexander and J. Yorke (Amer. J. Math., 100 (1978), 263–292). 相似文献
7.
I. S. Donskaya A. R. Kessel' S. S. Lapushkin 《Theoretical and Mathematical Physics》1994,98(1):100-106
Zubarev's nonequilibrium statistical operator method is used to construct a theory of the nonresonant acoustic absorption of the linear Ising magnet, the basic Hamiltonian of which is of the two-particle kind and is treated without approximations. The frequency dependence of the absorption is determined and found to differ analytically from the well-known Debye curve
D
() but for reasonable values of the physical parameters gives an envelope that agrees qualitatively with
D
().Kazan Physicotechnical Institute, Russian Academy of Sciences; Moscow Institute of Instrument Manufacture. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 1, pp. 149–159, January, 1994. 相似文献
8.
Dr. Alexander Kovačec 《Monatshefte für Mathematik》1981,92(1):19-35
We shall develop a method to prove inequalities in a unified manner. The idea is as follows: It is quite often possible to find a continuous functional :
n
, such that the left- and the right-hand side of a given inequality can be written in the form (u)(v) for suitable points,v=v(u). If one now constructs a map
n
n
, which is functional increasing (i.e. for each x
n
(which is not a fixed point of ) the inequality (x)<((x)) should hold) one specially gets the chain (u)(
u))(
2(u))...
n
(u)). Under quite general conditions one finds that the sequence {
n
(u)}
n converges tov=v(u). As a consequence one obtains the inequality (u)(v). 相似文献
9.
P. N. Müller K. -D. Reinsch R. Bulirsch 《Journal of Optimization Theory and Applications》1994,80(2):367-372
In Ref. 1, the author claimed that the problem y=y
3 is soluble only for a certain range of the parameter . An analytic approach, as adopted in the following contribution, reveals that a unique solution exists for any positive value of . The solution is given in closed form by means of Jacobian elliptic functions, which can be numerically computed very efficiently. In the limit 0+, the solutions exhibit boundary-layer behavior at both endpoints. An easily interpretable approximate solution for small is obtained using a three-variable approach. 相似文献
10.
V. I. Vasyunin 《Journal of Mathematical Sciences》2003,115(2):2093-2099
If T is a completely nonunitary contraction on a Hilbert space and L is its invariant subspace corresponding to a regular factorization of its characteristic function = , then L is hyperinvariant if and only if the following two conditions are fulfilled: (1) supp * supp is of Lebesgue measure zero; (2) for every pair A H
(E E) and A
* H
(E
* E
*) intertwining by , i.e., such that A =A
*, there exists a function A
F H
(F F) intertwining with A by and with A
* by , i.e., such that A = A
F and A
F = A
*. Bibliography: 4 titles. 相似文献
11.
V. N. Sudakov 《Mathematical Notes》1973,14(4):886-888
Let X and Y be locally compact-compact topological spaces, F X×Y is closed, and P(F) is the set of all Borel probability measures on F. For us to find, for the pair of probability measures (x, y P (X)×P(Y), a probability measure P(F) such that
X
=
X
–1
,
Y
=
Y
–1
it is necessary and sufficient that, for any pair of Borel sets A X, B Y for which (A× B) F=Ø, the condition
XA+
YB 1 holds.Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 573–576, October, 1973. 相似文献
12.
L. M. Gershtein 《Ukrainian Mathematical Journal》1993,45(10):1629-1635
The paper deals with the Cauchy problem for a complete second-order differential equation with unbounded operator coefficientsu+A(t)u+B(t)u=f, u(0)=u0, u(0)=u
1
. By using the commutant method, we construct a coercive solution of this problem in Holder space in the case where the operatorB is as strong as the operator A2.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1449–1454, October, 1993. 相似文献
13.
F. Schipp 《Analysis Mathematica》1990,16(2):135-141
H={h
1,I } — , . : , I ¦(I)¦=¦I¦, ¦I¦ — I. H H
={h
(I),I} . , , . L
p
.
Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday
This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153. 相似文献
Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday
This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153. 相似文献
14.
T. E. Pyasetskaya 《Journal of Mathematical Sciences》1993,67(4):3225-3228
We consider the behavior of a solution of the wave equation utt (t, x) – a2 (t) uxx (t, x)=f (t, x) with initial conditions u (0, x)=u0, /t6t u (t, x) ¦t=0
=u1 (x), a andf being random functions; a(t) characteristizes the variable character of the medium;f(t, x) is the inhomogeneity, having the character of random walks.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 75–78, 1988. 相似文献
15.
For a graphG, letp(G) andc(G) denote the length of a longest path and cycle, respectively. Let (t,n) be the minimum ofp(G), whereG ranges over allt-tough connected graphs onn vertices. Similarly, let (t,n) be the minimum ofc(G), whereG ranges over allt-tough 2-connected graphs onn vertices. It is shown that for fixedt>0 there exist constantsA, B such that (t,n)A·log(n) and (t,n)·log((t,n))B·log(n). Examples are presented showing that fort1 there exist constantsA, B such that (t,n)A·log(n) and (t,n)B· log(n). It is conjectured that (t,n) B·log(n) for some constantB. This conjecture is shown to be valid within the class of 3-connected graphs and, as conjectured in Bondy [1] forl=3, within the class of 2-connectedK
1.l-free graphs, wherel is fixed. 相似文献
16.
P. Révész 《Probability Theory and Related Fields》1992,93(1):21-37
Summary We say that the discD()R
2, of radius , located around the origin isp-covered in timeT by a Wiener processW(·) if for anyzD() there exists a 0tT such thatW(t) is a point of the disc of radiusp, located aroundz. The supremum of those 's (0) is studied for which,D() isp-covered inT. 相似文献
17.
Wolfgang Zimmermann 《manuscripta mathematica》1971,5(3):229-234
If u is a morphism, A an object of some category, we say, A is injective relative to u, iff Hom (u, A) is epi. In this paper we consider classesU of monomorphisms in categories of modules with the following property: if u, u are monos, such that uu exists and is inU, then u is inU. We show, that the closure a(U) ofU is an injective class in the sence of S. Eilenberg and J. C. Moore, that is, for each module A there is a mono a:AB, such that B is injective relative to u for all uU and that each module C, that is injective relative to u for all uU is injective relative to a. 相似文献
18.
A Note on the Oscillation of Second Order Differential Equations 总被引:1,自引:0,他引:1
We give a sufficient condition for the oscillation of linear homogeneous second order differential equation y + p(x)y + q(x)y = 0, where and is positive real number. 相似文献
19.
Fan Xianling 《数学学报(英文版)》1996,12(3):254-261
In this paper the regularity of the Lagrangiansf(x, )=||(x)(1<
1(x)2< +) is studied. Our main result: If(x) is Holder continuous, then the Lagrangianf(x, )=f(x, )=||(x) is regular. This result gives a negative answer to a conjecture of V. Zhikov.Supported by the National Natural Science Foundation of China. 相似文献
20.
Xiangsheng Xu 《Applied Mathematics and Optimization》1996,34(3):299-324
A partial regularity theorem is established for a particular class of weak solutions to the systemu/t– div(K(u)u)=(u)¦¦2, div((u))=0 on a bounded domain inR
N
. Under our assumptions, (u) may exhibit exponential decay, and thus the system may be degenerate. Our proof is based upon a blow-up argument.This work was supported in part by NSF Grant DMS9424448. 相似文献