共查询到20条相似文献,搜索用时 31 毫秒
1.
V. V. Zhuk 《Mathematical Notes》1968,4(1):500-508
Let n (f) and Pr (f) be, respectively, the Fejer and Poisson means of the Fourier series of the functionf. The present work considers problems associated with the rapidity of approximation of a continuous 2-periodic function by means of Fejer and Poisson processes, and gives, in particular, an upper bound to the deviation of the Fejer and Poisson processes from the function in terms of moduli of continuity, and a lower bound to n (f)–f in terms of functionals composed of best approximations to the functionf; in addition, some relationships among the quantities Pr (f)–f and n (f)–f are established.Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 21–32, July, 1968. 相似文献
2.
B. S. Kashin 《Mathematical Notes》1973,14(5):930-935
We will investigate the properties of series of functions which are unconditionally convergent almost everywhere on [0, 1]. We will establish the following theorem: If the series
k=1
f
k(x) converges unconditionally almost everywhere, then there exists a sequence {k}
1
,k , such that if
k
k
, k=1, 2,..., the series
k=1
k/k(x) converges unconditionally almost every-where.Translated from Mate matte heskie Zametki, Vol. 14, No. 5, pp. 645–654, November, 1973.The author wishes to thank Professor P. L. Ul'yanov for his help. 相似文献
3.
Dr. Johannes Schoißengeier 《Monatshefte für Mathematik》1979,87(1):21-52
In this paper we give the connection between the zeros of the -function and sequences(g(p)), p prime, mod 1 ifg(x)=x
for 0, >0 or ifg(X) is a polynomial in . 相似文献
4.
LetG be a subgroup of the general linear group GLn(K), where charK 2. Put Kn =V. AssumeG is generated by the setS of all elements inG for which dimV( – 1) = 1, and suppose 2=1V for each inS. If {V(–1)¦S} contains a simplex, if – 1V G, and if inG is a product of dim v(–1) elements inS wheneverV(–1) is not contained in the kernel of–1, thenG is a subgroup of an orthogonal group.This research was supported in part by NSERC Canada grant A7251.To Helmut Mäurer on his 60th birthday 相似文献
5.
W. Ricker 《Integral Equations and Operator Theory》1985,8(2):276-288
LetT be a continuous scalar-type spectral operator defined on a quasi-complete locally convex spaceX, that is,T=fdP whereP is an equicontinuous spectral measure inX andf is aP-integrable function. It is shown that (T) is precisely the closedP-essential range of the functionf or equivalently, that (T) is equal to the support of the (unique) equicontinuous spectral measureQ
* defined on the Borel sets of the extended complex plane * such thatQ
*({})=0 andT=zdQ
*(z). This result is then used to prove a spectral mapping theorem; namely, thatg((T))=(g(T)) for anyQ
*-integrable functiong: * * which is continuous on (T). This is an improvement on previous results of this type since it covers the case wheng((T))/{} is an unbounded set in a phenomenon which occurs often for continuous operatorsT defined in non-normable spacesX. 相似文献
6.
Albert Raugi 《Probability Theory and Related Fields》1988,77(4):481-496
Résumé SoitG un groupe moyennable connexe, locallement compact, à base dénombrable. Soit une mesure positive sur les boréliens deG. Nous étudions les fonctions boréliennes positivesh vérifiant: g G,
. Sous de bonnes hypothèses sur , nous obtenons, pour ces fonctions, une représentation intégrale à l'aide d'exponentielles.
Summary LetG be a connected locally compact separable amenable group. Let be a positive measure on the Borel -field ofG. We study the positive Borel functionsh onG which satisfy: g G, . Under smooth assumptions on , we establish an integral representation of these functions in term of exponentials.相似文献
7.
Let be a probability measure on a locally compact groupG. A real Borel functionf onG is called -harmonic if it satisfies the convolution equation *f=f. Given that isnonsingular with its translates, we show that the bounded -harmonic functions are constant on a class of groups including the almost connected [IN]-groups. If is nondegenerate and absolutely continuous, we solve the more general equation *= for positive measure on those groups which are metrizable and separable.Supported by Hong Kong RGC Earmarked Grant and CUHK Direct Grant 相似文献
8.
Stephen J. Gardiner 《Monatshefte für Mathematik》1992,114(2):97-106
Let (–1,1), let 2/(1–)p<, letp denote the Hölder conjugate ofp, and let be an open arc of the unit circle. It is shown that, iff is a holomorphic function on the unit disc such that: (i) (1–|z|)log+|f(z)| isL
p
-integrable on the sector {r:0f has an infinite asymptotic value has -finite (2–(1+)p)-dimensional Hausdorff, measure, thenf has finite angular limits on a subset of of positive linear measure. In fact, a stronger conclusion will be established. 相似文献
9.
Pavel Pyrih 《Potential Analysis》1994,3(3):273-281
We study the set of functions in quasi-analytic classes and the set of finely holomorphic functions. We show that no one of these two sets is contained in the other.LetI denote the set of complex functionsf: for which there exists a quasi-analytic classC{M
n} containingf. Let denote the set of complex functionsf: for which there exist a fine domainU containing the real line and a function
finely holomorphic onU satisfyingf(x)=
(x) for allx . The power of unique continuation is incomparable in these two cases (I\ is non-empty, \I is non-empty).Research supported by the grant No. 201/93/2174 of Czech Grant Agency and by the grant No. 354 of Charles University. 相似文献
10.
B E Johnson 《Integral Equations and Operator Theory》2001,40(4):454-464
For a probability measure on a locally compact groupG which is not supported on any proper closed subgroup, an elementF ofL
(G) is called -harmonic if F(st)d(t)=F(s), for almost alls inG. Constant functions are -harmonic and it is known that for abelianG all -harmonic functions are constant. For other groups it is known that non constant -harmonic functions exist and the question of whether such functions exist on nilpotent groups is open, though a number of partial results are known. We show that for nilpotent groups of class 2 there are no non constant -harmonic functions. Our methods also enable us to give new proofs of results similar to the known partial results. 相似文献
11.
It is shown that two real functionsf andg, defined on a real intervalI, satisfy the inequalitiesf(x + (1 – )y) g(x) + (1 – )g(y) andg(x + (1 – )y) f(x) + (1 – )f(y) for allx, y I and [0, 1], iff there exists an affine functionh: I such thatf h g. As a consequence we obtain a stability result of Hyers—Ulam type for affine functions. 相似文献
12.
We prove that the condition
is necessary and sufficient for the validity of the relation ln F() ln (, F), +, outside a certain set for every function from the class
. Here, H(, f) is the class of series that converge for all 0 and have a form
and f() is a positive differentiable function increasing on [0, +) and such that f(0) = 1 and ln f() is convex on [0, +). 相似文献
13.
For 1/2<<1 fixed, letE
(T) denote the error term in the asymptotic formula for
. We obtain some new bounds forE
(T), and an _-result which is the analogue of the strongest _-result in the classical Dirichlet divisor problem. 相似文献
14.
Let M
n =X1+...+Xn be a martingale with bounded differences Xm=Mm-Mm-1 such that {|Xm| m}=1 with some nonnegative m. Write 2=
1
2
+ ... +
n
2
. We prove the inequalities {M
nx}c(1-(x/)), {M
n x} 1- c(1- (-x/)) with a constant
. The result yields sharp inequalities in some models related to the measure concentration phenomena. 相似文献
15.
Lian-Xi Ku 《Southeast Asian Bulletin of Mathematics》2000,24(3):375-382
In this note, we prove that, for Robins boundary value problem, a unique solution exists if fx(t, x, x), fx(t, x, x), (t), and (t) are continuous, and fx -(t), fx -(t), 4(t) 2 + 2(t) ++ 2(t), and 4(t) 2 + 2(t) + 2(t).AMS Subject Classification (2000) 34B15 相似文献
16.
V. Yu. Popov 《Mathematical Notes》1973,14(6):1085-1092
Let
be the best mean-square approximation of a functionf(x) L2(Rm) (m=1, 2, ...) by integral functions of the exponential spherical type (in the sense of thel
q metric, 0
>0, where(f,/; l p)L2(Rm) is the spherical (in the sense of the metricl p, 0f(x) L2(Rm). For the quantity two-sided estimates are obtained which are uniform in the parameters m, q, and p. Similar results are also obtained in the case of q=p=2 for classes of functions W f2 (Rm) (=1,2,...).Translated from Matematicheskie Zametki, Vol. 14, No. 6, pp. 913–924, December, 1973.The author would like to express his deep gratitude to N. I. Chernykh under whose guidance this work has been carried out. 相似文献
17.
A. V. Vasin 《Journal of Mathematical Sciences》1994,71(1):2180-2191
The fundamental result: for an arbitrary bounded, simply connected domain in , the subspace Ln,m
p() of the space Lp(, ) ( is the plane Lebesgue measure, p 1), consisting of the (m, n)-analytic functions in , is complemented in LP(, ) (a function f is said to be (m, n)-analytic if (m+n/¯ZmZn)f=0 in ). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyski, the space Ln,m
P() is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic LP-functions in is complemented in LP(, ). This result has been known earlier only for smooth domains.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 190, pp. 15–33, 1991. 相似文献
18.
We consider the boundary-value problem u
tt + u
t + (1 + cos2)sin u =2
u
xx, u
x|x=0=ux|x==0, where 0<1, =(1+)t, ,> 0, and the sign of is arbitrary. It is proved that for an appropriate choice of the external parameters and and for sufficiently small the number of exponentially stable solutions 2-periodic in can be made equal to an arbitrary predefined number. 相似文献
19.
Héctor H. Cuenya 《Analysis Mathematica》2000,26(3):175-186
Let (, A, ) be a measure space, a function seminorm on M, the space of measurable functions on , and M
the space {f M : (f) < }. Every Borel measurable function : [0, ) [0, ) induces a function : M M by (f)(x) = (|f(x)|). We introduce the concepts of -factor and -invariant space. If is a -subadditive seminorm function, we give, under suitable conditions over , necessary and sufficient conditions in order that M
be invariant and prove the existence of -factors for . We also give a characterization of the best -factor for a -subadditive function seminorm when is -finite. All these results generalize those about multiplicativity factors for function seminorms proved earlier. 相似文献
20.
, n- n- 1 , . , , ( « ») f . 相似文献