共查询到20条相似文献,搜索用时 31 毫秒
1.
Henrik Stetkaer 《Aequationes Mathematicae》1997,53(1-2):91-107
Summary We find the complete set of continuous solutionsf, g of Wilson's functional equation
n = 0
N – 1
f(x + wny) = Nf(x)g(y), x, y C, given a primitiveN
th rootw of unity.Disregarding the trivial solutionf = 0 andg any complex function, it is known thatg satisfies a version of d'Alembert's functional equation and so has the formg(z) = g
(z) = N–1
n = 0
N – 1
E(wnz) for some C2. HereE
(1, 2)(x + iy) = exp(
1x + 2).For fixedg = g
the space of solutionsf of Wilson's functional equation can be decomposed into theN isotypic subspaces for the action of Z
N
on the continuous functions on C. We prove that ther
th component, wherer {0, 1, ,N – 1}, of any solution satisfies the signed functional equation
n = 0
N – 1
f(x + wny)wnr = Ng(x)f(y), x, y C. We compute the solution spaces of each of these signed equations: They are 1-dimensional and spanned byz
n = 0
N – 1
wnr E(wnz), except forg = 1 andr 0 where they are spanned by
andz
N – r. Adding the components we get the solution of Wilson's equation. Analogous results are obtained with the action ofZ
N on C replaced by that ofSO(2).The case ofg = 0 in the signed equations is special and solved separately both for Z
N
andSO(2). 相似文献
2.
Marguerite-Marie Virotte-Ducharme 《Geometriae Dedicata》1993,45(2):121-162
In this paper we give Coxeter presentation (X, ) for the three Fischer groupsG=Fi22, Fi23, Fi24; we apply methods exposed in the first part. Each of these groups is generated by a class of 3-transpositions (named here a Fischer class) in which elements ofX are chosen. A subset of is the set of all the relations (xy)
m(x,y)=1, wherex andy are inX and wherem(x,y) means the order ofxy inG. We obtainG as a specified quotient of the Coxeter group (X, ) with the appropriate diagram . 相似文献
3.
Chih-Wen Weng 《Graphs and Combinatorics》1995,11(2):201-207
LetY = (X, {R
i
}
oid) denote aP-polynomial association scheme. By a kite of lengthi (2 i d) inY, we mean a 4-tuplexyzu (x, y, z, u X) such that(x, y) R
1,(x, z) R
1,(y, z) R
1,(u, y) R
i–1,(u, z) R
i–1,(u, x) R
i. Our main result in this paper is the following. 相似文献
4.
The work is related to the problem by P. Erds about the estimation of the numbers
as N.We shall deal with the case where the z
j are all possible roots of the unity ordered in such a way that all the roots of degree n follow the roots of degree n-1. Within the group of roots of degree n, the enumeration can vary. We prove that ln A
N grows like N, and we get estimates of possible values of the lower limit of the ratio (ln A
N
/N as well as exact bounds of the upper limit of this ratio. 相似文献
5.
S. V. Shvedenko 《Mathematical Notes》1977,21(4):281-284
The sequence spaceH
P
(z)={{f (zh)}:f H
p} is defined for a fixed sequence Z={zk} of different points of the open unit disk and the Hardy class HP of analytic functions in the disk. For an arbitrary p[1, ) is constructed a point sequence Z= {zk} such that 1h
p(z), but r hp (Z) for r > 1. It follows from a well-known result of L. Carleson that the inclusions r h (Z) for all r[1,] are equivalent.Translated from Matematicheskie Zametki, Vol. 21, No. 4, pp. 503–508, April, 1977. 相似文献
6.
I. E. Chizhikov 《Journal of Mathematical Sciences》1999,96(2):2980-2984
For an arbitrary (0, 1/2) we construct a functionf(z) of lower order [f]=. that is meromorphic in the disk D = {z ¦z¦< 1} and such that the set (f) of positive deflections of the functionf (in the sense of V. P. Petrenko) has positive logarithmic capacity.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 48–53. 相似文献
7.
Donald I. Cartwright 《Monatshefte für Mathematik》1992,113(3):183-188
LetX be a countable discrete group and let be an irreducible probability onX. The radius of convergence of the Green function
is finite, and independent ofx. Let
0} \right\}$$
" align="middle" border="0">
be the period of . We show that for eachxX the singularities of the analytic functionzG(x; z) on the circle {z:|z|=} are precisely the points e
2ik/d
k=0, ...,d–1. In particular, is the only singularity on the circle in the aperiodic cased=1 (which occurs, for example, when (e)>0). This affirms a conjecture ofLalley [5]. When is symmetric, i.e., (x
–1)=(x) for allxX, d is either 1 or 2. As another particular case of our result, we see that- is then a singularity ofzG (x; z) if and only ifd=2, in which caseX is bicolored. This answers a question ofde la Harpe, Robertson andValette [2]. 相似文献
8.
This work deals with the guidance and control of a system which is composed of a rolling disk and a controlled slender rod that is pivoted, through its center of mass, about the disk center. There are given N points P
i, i=1, ..., N, in the horizontal plane, a set of angles 2i
, i=1, ..., N, a finite-time interval [0, t
f], and a sequence of times 1=0<2<...<
N
=t
f. Using the concept of path controllability, a closed-loop control law is derived to steer the system in such a manner that the disk center and the rod angle of rotation 2 will pass through (P
i, 2i
) at the times
i
, i=1,...,N, respectively. This system serves as a model for the motion of a simple mobile robot. 相似文献
9.
S. V. Solov'ev 《Journal of Mathematical Sciences》1982,20(4):2367-2369
We consider the (&, )-fragment of the intuitionistic propositional calculus. It is proved that under the standard transformation of a Gentzen derivation into a natural derivation(), the length of (())22·length(
). There is constructed a sequence of Gentzen derivations of length i, for which the length of ((
i))21/3·length(i), which shows that the upper bound obtained is not too weak.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 192–196, 1979. 相似文献
10.
We establish a criterion for the existence of a solution of the interpolation problem f(
n
) = b
n in the class of functions f analytic in the unit disk and satisfying the relation
where : [1; +) (0; +) is an increasing function such that the function ln(t) is convex with respect to lnt on the interval [1; +) and lnt = o(ln(t)), t . 相似文献
11.
I. A. Ibragimov 《Journal of Mathematical Sciences》1982,20(3):2164-2175
Let be a Gaussian random vector with values in a Hilbert space H. We denote by(a, z) the ball in H with center ata and of radius z. Some asymptotic formulas for I (a, z)=P (a, z), z 0, are presented in the paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 85, pp. 75–93, 1979. 相似文献
12.
Dr. Jean-Pierre Kahane 《Monatshefte für Mathematik》1982,93(4):289-292
Given a non-empty closed subsetF of the unit circle |z|=1, and a Möbius transformationM(z) of the unit disc |z|1, such thatM(0)0, there exists a functionf(z) holomorphic in the unit disc,F being the singular set at the boundary, whose Taylor coefficients tend to zero while the Taylor coefficients off(M(z)), do not tend to zero. 相似文献
13.
Graham R. Brightwell 《Graphs and Combinatorics》1990,6(2):111-131
Posets
are said to be (positively) correlated with respect to a third posetR onX (we writeA
R
B) ifP(AR) P(AR B). HereP(CR) is the probability that a randomly chosen linear extension ofR is also a linear extension ofC. We classify posetsR onX such that(x, y)
s
(u, v) holds for all posetsS onX which are subposets ofR, wherex, y, u, v are distinct elements ofX. On the way to proving this result, we show when a correlation inequality due to Shepp holds strictly. 相似文献
14.
Dr. Karl Umgeher 《Monatshefte für Mathematik》1976,81(4):311-314
We consider the set of regular functions
. We construct a Borel measure and a class of outer measures
h
onH. With these and
h
we show that: (HS)=0 and
h
(HS)=0, (S is the set of normed univalent functions). From
h
(HS)=0 follows—forh=t
—that the Hausdorff—Billingsley-dimension ofHS is zero. 相似文献
15.
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
16.
P. D. Seymour 《Combinatorica》1995,15(2):281-288
LetG be a digraph, and letk1, such that no fractional packing of directed circuits ofG has value >k, when every vertex is given capacity 1. We prove there is a set ofO (k logk logk) vertices meeting all directed circuits ofG. 相似文献
17.
N. G. Karpova 《Mathematical Notes》1998,64(1):55-62
LetG be a domain in
n
,n2, letA be a connected complex (n–1)-dimensional submanifold ofG, and let be a plurisubharmonic function inGA. We obtain conditions on the growth of that guarantee the local boundedness of at a point a A G and the existence of a plurisubharmonic extension of toG.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 64–72, July, 1998.The author wishes to express her gratitude to Professor E. M. Chirka for numerous useful discussions and for his assistance in writing the present text. 相似文献
18.
M. N. Sheremeta 《Ukrainian Mathematical Journal》1990,42(5):591-595
For a function f analytic in a disk {z ¦ z ¦ <R }, 0 <R + , a criterion is obtained, in terms of the Taylor coefficients of the function, for the validity of the relation
(r) ln+
M (r)dr < + , whereM (r)= max {¦ (f (z) ¦ ¦z ¦=r < R}, and is a function positive on [0, R) and satisfying certain conditions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 5, pp. 668–673, May, 1990. 相似文献
19.
On a finite segment [0, l], we consider the differential equation
with a parameter C. In the case where a(x), (x) L
[0, l],
j
(x) L
1[0, l], j = 1, 2, a(x) m
0 > 0 and (x) m
1 > 0 almost everywhere, and a(x)(x) is a function absolutely continuous on the segment [0, l], we obtain exponential-type asymptotic formulas as
for a fundamental system of solutions of this equation. 相似文献
20.
E. P. Dolzhenko 《Mathematical Notes》1996,60(2):130-136
Letd(;z, t) be the smallest diameter of the arcs of a Jordan curve with endsz andt. Consider the rapidity of decreasing ofd(;)=sup{d(;z, t):z, t , ¦z–t¦} (as 0,0) as a measure of nicety of . Letg(x) (x0) be a continuous and nondecreasing function such thatg(x)x,g(0)=0. Put¯g(x)=g(x)+x, h(x)=(¯g(x))2. LetH(x) be an arbitrary primitive of 1/h
–1(x). Note that the functionH
–1
x is positive and increasing on (–, +),H
–1 0 asx– andH
–1+ asx +. The following statement is proved in the paper.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 176–184, August, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00236 and by the International Science Foundation under grant No. NCF000. 相似文献