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1.
Let { n} be a sequence of identically distributed independent random variables, M1=<0, M
1
2
<; S
0=0, S
n
= 1+ 2,+...+
n, n1; ¯ S=sup {S
n
n=0.} The asymptotic behavior of P(¯ St) as t is studied. If
t
P
( 1x dx=0((t)), then P(¯ St)– 1/¦¦
t
P ( 1x dx=0((t)) (t) is a positive function, having regular behavior at infinity.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 763–770, November, 1977.The author thanks B. A. Rogozin for the formulation of the problem and valuable remarks. 相似文献
2.
Let P n, nIN{0}, be probability measures on a-field A; f n, nIN{0}, be a family of uniformly bounded A-measurable functions and A
n, nIN, be a sequence of sub--fields of A, increasing or decreasing to the-field A
o. It is shown in this paper that the conditional expectations converge in P o-measure to with k, n, m , if P n| A, nIN, converges uniformly to P n| A and f n, nIN, converges in P o-measure to f o. 相似文献
3.
Let be an inner function, let C, ¦¦=1. Then the harmonic function [(+)]/(–)] is the Poisson integral of a singular measure
D. N. Clark's known theorem enables us to identify in a natural manner the space H 2 H 2 with the space L 2
(
).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 7–33, 1989. 相似文献
4.
An investigation of the approximation on [0, 1] of functions f (x) by spline functions s( f, ; x) of degree 2r-1 and of deficiency r (r>1) depending on the vector function =
1 (x),...,
r-1(x) and interpolating f (x) at fixed points. For the optimal choice of the vector
0, exact estimates are obtained of the norms f(x)-s ( f,
0; x) C[0,1] and f (x)-s ( f,
0; x) L[0, 1] on the function classes H
Translated from Matematicheskie Zametki, Vol. 8, No. 1, pp. 41–46, July, 1970.In conclusion we would like to thank N. P. Korneichuk for suggesting this problem and for his valuable advice. 相似文献
5.
For a mean zero norm one sequence ( f
n
) L
2[0, 1], the sequence ( f
n
{ nx+ y}) is an orthonormal sequence in L
2([0, 1] 2); so if
, then
converges for a.e. ( x, y)[0, 1] 2 and has a maximal function in L
2([0, 1] 2). But for a mean zero fL
2[0, 1], it is harder to give necessary and sufficient conditions for the L
2-norm convergence or a.e. convergence of
. If c
n
0 and
, then this series will not converge in L
2-norm on a dense G
subset of the mean zero functions in L
2[0, 1]. Also, there are mean zero fL [0, 1] such that
never converges and there is a mean zero continuous function f with
a.e. However, if f is mean zero and of bounded variation or in some Lip() with 1/2<1, and if | c
n
| = 0( n
–) for >1/2, then
converges a.e. and unconditionally in L
2[0, 1]. In addition, for any mean zero f of bounded variation, the series
has its maximal function in all L
p[0, 1] with 1 p<. Finally, if ( f
n
) L
[0, 1] is a uniformly bounded mean zero sequence, then
is a necessary and sufficient condition for
to converge for a.e. y and a.e. ( x
n
)[0, 1]. Moreover, if fL
[0, 1] is mean zero and
, then for a.e. ( x
n
)[0, 1],
converges for a.e. y and in all L
p
[0, 1] with 1 p<. Some of these theorems can be generalized simply to other compact groups besides [0, 1] under addition modulo one. 相似文献
6.
Let R(r, m) be the rth order Reed-Muller code of length 2
m
, and let ( r, m) be its covering radius. We prove that if 2 k m - r - 1, then ( r + k, m + k) ( r, m + 2( k - 1). We also prove that if m - r 4, 2 k m - r - 1, and R( r, m) has a coset with minimal weight ( r, m) which does not contain any vector of weight ( r, m) + 2, then ( r + k, m + k) ( r, m) + 2 k(. These inequalities improve repeated use of the known result ( r + 1, m + 1) ( r, m).This work was supported by a grant from the Research Council of Wright State University. 相似文献
7.
H
( G), f( g) H
( G) , ( , 1)- OHMC G. , OHMC, A. H. . , . , OHMC, lim sup p
n=, , , n .. . , 117 234 . . - 相似文献
8.
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), where u 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) when M=1 while the case N=1 is (a special case of) a theorem by J. Moser on minimal foliations of codimension 1 on a torus T
M
+1. In the autonomous case, f= f( x), the above result holds for any . 相似文献
9.
We obtain sufficient conditions for the absolute convergence of Fourier series for functions of L
d
2
depending on the properties of the function being expanded and the rate of growth of the sums
of the system of functions { k(t)} orthonormalized in [ a, b] with respect to d(t). We show that if at some point x [a, b] the function (t) has a discontinuity, at that point the Fourier series of any function f(t) L
d
2
, converges absolutely.Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 511–516, November, 1972. 相似文献
10.
Moser-type estimates for functions whose gradient is in the Lorentz space L(n, q), 1 q, 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), 2 q.Work partially supported by MURST (40%). 相似文献
11.
Zusammenfassung Für Randwertaufgaben der Form –u–l
0
...u–l
0
...u=f(x, u) mit l
0R, lR, f definiert und stetig auf { a<-x<-b, |u|<} wird eine Existenzaussage gewonnen, falls f in u linear durch die aufeinanderfolgenden Eigenwerte der zugehörigen linearen Aufgabe beschränkt ist. Zum Beweis betrachtet man die äquivalente Hammersteinsche Integralgleichung mit nichtsymmetrischem Kern. Mit Hilfe des Schauderschen Fixpunktsatzes erhält man für diese Integralgleichung Existenzaussagen, welche Ergebnisse von Dolph verallgemeinern.
Summary This note contains an existence theorem for a two-point boundary value problem of the form–u–l
0
u–l
0
u=f(x, u) wherel
0R,l
0R,f defined and continuous on {a<-xb, |u|<} iff is linear bounded inu by the successive eigenvalues of the corresponding linear problem. To prove this result we consider the equivalent Hammerstein integral equation with non-symmetric kernel. Schauders fixpoint principle supplies existence theorems for integral equations of this type which generalize results of Dolph in some sense. 相似文献
12.
Let f C[a, b]. Let P be a subset of C[a, b], L b – a be a given real number. We say that p P is a best approximation to f from P, with arc length constraint L, if A[p]
b
a
[1 + (p(x))
2] dx L and p – f q – f for all q P with A[q] L. represents an arbitrary norm on C[a, b]. The constraint A[p] L might be interpreted physically as a materials constraint.In this paper we consider the questions of existence, uniqueness and characterization of constrained best approximations. In addition a bound, independent of degree, is found for the arc length of a best unconstrained Chebyshev polynomial approximation.The work of L. L. Keener is supported by the National Research Council of Canada Grant A8755. 相似文献
13.
Summary Consider f+
ff+ (1– f2)+
f=0 together with the boundary conditions f(0)= f(0)=0, f ()=1. If =–1, >0, arbitrary there is at least one solution which satisfies 0< f<1 on (0, ). By the additional condition f>0 on (0, ) or, alternately 0< 1, the uniqueness of the solution is demonstrated.If =1, <0, arbitrary the existence of solutions for which –1< f<0 in some initial interval (0, t) and satisfying generally f>1 is established. In both problems, bounds for f (0) and qualitative behavior of the solutions are shown.
Sommario Si consideri il problema definito dall'equazionef+
f
f+ (1–f2)+
f=0 e dalle condizioni al contornof(0)=f (0)=0,f()=1. Assumendo=–1,>0, arbitrario si dimostra che esiste almeno una soluzione che soddisfa 0<f<1 nell'intervallo (0, ). Se in aggiunta si ipotizzaf>0 in (0, ), oppure 0<=1, l'unicità délia soluzione è assicurata.Successivamente si considéra il problema di valori al contorno con=1,<0, arbitrario. In questo caso esiste un'intera classe di soluzioni che soddisfano –1<f<0 in un intorno dell'origine e tali chef>1, in generale.Di detti problemi viene studiato il comportamento délle soluzioni e vengono determinate dalle maggiorazioni e minorazioni del valoref(0). 相似文献
14.
Let R(r, m) by the rth order Reed-Muller code of length 2
m
, and let ( r, m) be its covering radius. We obtain the following new results on the covering radius of R(r, m): 1. ( r+1, m+2) 2( r, m)+2 if 0 rm–2. This improves the successive use of the known inequalities ( r+1, m+2)2( r+1, m+1) and ( r+1, m+1) ( r, m).2.(2, 7)44. Previously best known upper bound for (2, 7) was 46. 3. The covering radius of R(1, m) in R( m–1, m) is the same as the covering radius of R(1, m) in R( m–2, m) for m4. 相似文献
15.
Let u(x,t) be a solution, uA|u| p for xIR 3, t0 where is the d'Alembertian, and A, p are constants with A>0, 1 0–|x–x0|, if the initial data u(x,0), ut(x,0) have their support in the ball |x–x0|t0. In particular global solutions of u=A|u|p with initial data of compact support vanish identically. On the other hand for A>0, p>1+2 global solutions of u=A|u|p exist, if the initial data are of compact support and u is sufficiently small in a suitable norm. For p=2 the time at which u becomes infinite is of order u–2.Dedicated to Hans Lewy and Charles B. Morrey, Jr.The research for this paper was performed at the Courant Institute and supported by the Office of Naval Research under Contract No. N00014-76-C-0301. Reproduction in whole or part is permitted for any purpose of the United States Government. 相似文献
16.
Résumé On étudie, sans hypothèse de convexité, les équations f=g, f=g et f=g.
Summary We study, without any convexity hypothesis, equations f=g, f=g and f=g where and respectively denote infimal convolution and deconvolution. We give an explicit formulation of these results in the quadratic hilbertian frame, and we interpret them in terms of parallel addition and subtraction of non necessarily semi-definite positive operators. 相似文献
17.
In this paper, by exploiting recent results on the pathwise behavior of the workload process in single server, work conserving queues of the G/G/1/ type, we show that the workload of multiserver, work conserving queues of G/G/m/ (m<) (and G/G/) queues satisfies an o( t) growth condition, provided that the time average of the work brought into the system is less than m for m < (and finite for m=). 相似文献
18.
We show that a multiplication operator ( T)= ATB is normality preserving if and only if it is hyponormality preserving, if and only if it is either of the form A= fg, B= h f, or A= D, B= D* for some C and D* D=I. Also we show that is (semi-) Fredholmness prserving if and only if A and B are (semi-) Fredholm operators.Supported by the Science Foundation of Zhejiang Province and NSF. 相似文献
19.
We give uniform estimates of entire functions of exponential type less than having sufficiently small logarithmic sums over real sequences {
n
} satisfying |
n
– n| L and
n+1–
n
for fixed positive constants L and . We thereby generalize results about logarithmic sums over the set of integers and so-called relatively h-dense sequences. 相似文献
20.
In the standard 4( O
n
) model, a critical regime in which the coupling constant g of the 4 decreases as a certain given power as T-T
c0 is considered. From the point of view of physics, such a formulation of the problem corresponds to a certain class of trajectories of approach to the triple point in the two-dimensional plane of the physical parameters of the system. It is shown that in such a modified critical regime all the critical dimensions can be expressed in terms of the specified value of the exponent and the ordinary critical dimensions of the 4 model known in the form of 4- expansions.Leningrad State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 168–172, April, 1992. 相似文献
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