共查询到20条相似文献,搜索用时 171 毫秒
1.
A. V. Kroo 《Mathematical Notes》1977,22(1):536-546
Suppose thatk, rz+, W
o
r
H[]C= {ff is a 2-periodic function,f Cr [–, ], (f(r), ) ()}, Tk is the space of trigonometric polynomials of order k, pk(f)Tk is the polynomial of best uniform approximation to f, and Ek(f) is the error of the best approximation. It is shown that for an arbitrary > 0 we have,where for 0<⩽(1),k > 0.R () is the root of the equation
, and for k = 0 or > (1) we have R()=.Translated from Matematicheskie Zametki, Vol. 22, No. 1, pp. 85–101, July, 1977.The author thanks S. B. Stechkin for posing the problem and for his attention to this work. 相似文献
2.
L. Chierchia C. Falcolini 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(2):210-220
We extend a recent method of proof of a theorem by Kolmogorov on the conservation of quasi-periodic motion in Hamiltonian systems so as to prove existence of (uncountably many) real-analytic quasi-periodic solutions for elliptic systems u=f
x
(u, y), whereu y
M
u(y)
N
,f=f(x, y) is a real-analytic periodic function and is a small parameter. Kolmogorov's theorem is obtained (in a special case) whenM=1 while the caseN=1 is (a special case of) a theorem by J. Moser on minimal foliations of codimension 1 on a torusT
M
+1. In the autonomous case,f=f(x), the above result holds for any . 相似文献
3.
Dr. E. Tarafdar 《Monatshefte für Mathematik》1976,82(4):341-344
Iff is a self mapping on a closed convex subsetK of a separated quasicomplete locally convex linear topological spaceE such that (i)E is strictly convex, (ii)f (K) is contained in a compact subset ofK and (iii)f satisfies a contraction condition, then it is shown that for eachxK, the sequence of {U
n
(x)}
n
=1 of iterates, whereU
KK is defined byU
(y)=f(y)+(1-) y, yK, converges to a fixed point off. 相似文献
4.
This article studies nonlocal problems for equations of motion of Kelvin-Voight fluids (2): 1) global solvability of initial-boundary-value problem (2)-(3) on halfaxisR
+ with free termf(x, t) S2(+; L2(0)) (see (4)); 2global solvability of system (2) on the entire axis
R
in the class of functions that are bounded as t±with free term
f(x,t)S2(; L2());3) the existence of periodic solutions for system (2) that are periodic in t with period with free term,f(x,t)L2((0,); L2());4) the existence of solutions of system (2) that are almost periodic in t with free term
f(x,t)S2(, L2()).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 185, pp. 111–124, 1990. 相似文献
5.
Let {W(s)}
s
0 be a standard Wiener process. The supremum of the squared Euclidian norm Y (t)2, of the R2-valued process Y(t)=(1/t
W(t), {12/t
3 int0
t
s dW (s)– {3/t} W(t)), t [, 1], is the asymptotic, large sample distribution, of a test statistic for a change point detection problem, of appearance of linear trend. We determine the asymptotic behavior P {sup
t
[, 1] Y(t)2 > u as u , of this statistic, for a fixed (0,1), and for a moving = (u) 0 at a suitable rate as u . The statistical interest of our results lie in their use as approximate test levels. 相似文献
6.
Klaus-Jürgen Eckardt 《manuscripta mathematica》1976,18(1):43-55
The problem of existence of wave operators for the Klein-Gordon equation (
t
2
–+2+iV1t+V2)u(x,t)=0 (x R
n,t R, n3, >0) is studied where V1 and V2 are symmetric operators in L2(R
n) and it is shown that conditions similar to those of Veseli-Weidmann (Journal Functional Analysis 17, 61–77 (1974)) for a different class of operators are also sufficient for the Klein-Gordon equation. 相似文献
7.
N. L. Gordeev 《Journal of Mathematical Sciences》2003,116(1):2961-2971
Let be a linear representation of a finite group over a field of characteristic 0. Further, let R
be the corresponding algebra of invariants, and let P
(t) be its Hilbert–Poincaré series. Then the series P
(t) represents a rational function (t)/(t). If R
is a complete intersection, then (t) is a product of cyclotomic polynomials. Here we prove the inverse statement for the case where is an almost regular (in particular, regular) representation of a cyclic group. This yields an answer to a question of R. Stanley in this very special case. Bibliography: 3 titles. 相似文献
8.
We consider the function space B
p
l
() of functionsf(x), defined on the domain of a certain class and characterized by specific differential-difference properties in Lp(). We prove a theorem on the embedding B
p,q
l
() Lq in the case whenl=n/p –n/q >0 and its generalization for vectorl, p, q.Translated from Matematicheski Zametki, Vol. 6, No. 2, pp. 129–138, August, 1969. 相似文献
9.
Moser-type estimates for functions whose gradient is in the Lorentz space L(n, q), 1q, are given. Similar results are obtained for solutions uH
inf0
sup1
of Au=(f
i
)
x
i
, where A is a linear elliptic second order differential operator and |f|L(n, q), 2q.Work partially supported by MURST (40%). 相似文献
10.
L. D. Berkovitz 《Journal of Optimization Theory and Applications》1974,14(5):521-528
A lower closure theorem for an abstract control problem is proved. The functional isJ(,u)=
G
f
0(t, (M)(t),u(t))dt and the state equations areN(t)=f(t, (M)(t),u(t)). It is shown that, if {(
k
,u
k)} is a sequence of admissible controlsu
k and corre-sponding trajectories
k
such that lim infJ(
k
,u
k)<+ and such that
k
weakly,M
k
M strongly,N
k
N weakly, and {u
k} is bounded in someL
p norm, then there is a controlu such that (,u) is admissible and lim infJ(
k
,u
k)J(,u).Dedicated to Professor M. R. HestenesThis research was supported by the National Science Foundation, Grant No. GP-33551X. 相似文献
11.
Z. A. Chanturiya 《Mathematical Notes》1978,23(2):123-127
Let (n) be a system, close to the orthonormal complete system (x
n). An estimate is obtained for the deviation of the system {fn}, obtained from {n} by Schmidt's method, from the system {xn}. This estimate is used to show that, in any LP(–1,1), withp (1,4/3] [4,), and for any >e¦4 = i,13..., there exists an orthogonal algebraic system (P
n
(x))
n=0
, forming a basis in LP and such that n = degP
n
(x) n for n>no(p,).Translated from Matematicheskie Zametki, Vol. 23, No. 2, pp. 223–230, February, 1978. 相似文献
12.
Xiuchun Li 《应用数学学报(英文版)》1987,3(4):374-383
In this paper we give a complete asymptotic expansion of the Jacobi functions
(, )
(t) as + . The method we employed to get the complete expansion follows that of Olver in treating similar problems. By using a Gronwall-Bellman type inequality for an improper integral in which the integrand is an unbounded function and contains a parameter, we get an error bound of the asymptotic approximation which is different from that of Olver's. 相似文献
13.
In this paper we study initial value problems likeu
t–R¦u¦m+uq=0 in n× +, u(·,0+)=uo(·) in N, whereR > 0, 0 <q < 1,m 1, andu
o is a positive uniformly continuous function verifying –R¦u
o¦m+u
0
q
0 in
N
. We show the existence of the minimum nonnegative continuous viscosity solutionu, as well as the existence of the function t(·) defined byu(x, t) > 0 if 0<t<t
(x) andu(x, t)=0 ift t
(x). Regularity, extinction rate, and asymptotic behavior of t(x) are also studied. Moreover, form=1 we obtain the representation formulau(x, t)=max{([(u
o(x – t))1–q
–(1–q)t]+)1/(1–q): ¦¦R}, (x, t)
+
N+1
.Partially supported by the DGICYT No. 86/0405 project. 相似文献
14.
Let
n
be n-dimensional Euclidean space, and let : [0, L]
n
and : [0, L]
n
be closed rectifiable arcs in
n
of the same total length L which are parametrized via their arc length. is said to be a chord-stretched version of if for each 0s tL, |(t)–(s)| |(t)–(s)|. is said to be convex if is simple and if ([0, L]) is the frontier of some plane convex set. Individual work by Professors G. Choquet and G. T. Sallee demonstrated that if were simple then there existed a convex chord-stretched version of . This result led Professor Yang Lu to conjecture that if were convex and were a chord-stretched version of then and would be congruent, i.e. any chord-stretching map of a convex arc is an isometry. Professor Yang Lu has proved this conjecture in the case where and are C
2 curves. In this paper we prove the conjecture in general. 相似文献
15.
Radu Păltănea 《Journal of Computational Analysis and Applications》2003,5(2):195-235
We obtained that for any n N, C = 1 is the smallest constant for which the inequality ||B
n
(f) - f|| C 2(f, 1/n) holds on the class of continuous functions f, as well as on the class of bounded functions f, where B
n
is the Bernstein operators of degree n, 2 is the second order modulus and || || is the sup-norm. 相似文献
16.
Michele Carriero Antonio Lead Franco Tomarelli 《Calculus of Variations and Partial Differential Equations》1994,2(2):219-240
Given a regular bounded open set R
2,, >0 andg L
q
() withq>2, we prove, under compatibility and safe load conditions ong, the existence of a minimizing pair for the functional, over closed setsK 2 and functionsu C0(
) C2(/K); here ¦[Du]¦ denotes the jump ofDu acrossK and 1 is the 1-dimensional Hausdorff measure.Dedicated to Enrico Magenes for his 70th birthday 相似文献
17.
Shiqi Song 《应用数学学报(英文版)》1993,9(2):115-124
LetX be the solution of the SDE:dX
t = (X
t)dB
t +b(X
t)dt, with andb C
b
(R) such that >0 for some constant , andB a real Brownian motion. Let be the law ofX onE=C([0, 1],R) andk E* – {0}, whereE* is the topological dual space ofE. Consider the classical form:
k
(u, v)=u / kv / kd, whereu andv are smooth functions onE. We prove that, if
k
is closable for anyk in a dense subset ofE* and if the smooth functions are contained in the domain of the generator of the closure of
k
, must be a constant function. 相似文献
18.
A. K. Guts 《Mathematical Notes》1973,13(5):411-415
Let n be n-dimensional Lobachevskii space, and {lx:x n} be a family of lines, parallel to a linel
0, 0n (in a given direction). Let {cx:Xn} be a family of circular cones in n of opening with axes lX and vertex X. Then, iff:nn(n>2) is a bijective mapping andf(Cx)=C
f(x), it follows thatf is a motion in the space n.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 687–694, May, 1973. 相似文献
19.
Let (K(s,t), 0s1, t1) be a Kiefer process, i.e., a continuous two-parameter centered Gaussian process indexed by [0,1]×+ whose covariance function is given by
(K(s1,t1) K(s2,t2))=(s1s2-s1s2)t1t2, 0s1, s21, t1, t2 0. For each t>0, the process K(·,t) is a Brownian bridge on the scale of
. Let M
1
*
(t) M
2
*
(t) M
j
*
(t) 0 be the ranked excursion heights of K(,t). In this paper, we study the path properties of the process tM
j
*
(t). Two laws of the iterated logarithm are established to describe the asymptotic behaviors of M
j
*
(t) as t goes to infinity. 相似文献
20.
Peter Schroth 《Aequationes Mathematicae》1985,28(1):252-254
LetG be a vector space over the field of rational numbers andf, g:G -linear mappings. equipped with the usual norm topology. Denote by
f
,
g
the initial topologies onG induced byf respectivelyg.Then the following result holds: If there is a nonvoid open setU whose complement contains at least one inner point such thatf
–1
U
g
, then there is ac withf=cg. In particular, iff0, the topologies coincide.Furthermore, a -linear mappingh: (G,
f
)(G,
g
) is continuous if and only if there is a real constantc withg
o
h=cf.Dedicated to Professor János Aczél on his 60th birthday 相似文献