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1.
Let k be a commutative ring, GG finite affine algebraic k-groups, and HH the dual Hopfalgebras of the affine algebras of G resp. G. The main results of this paper are: (I) If k is semilocal (e.g. k a field) there is an H-linear, HH-colinear, unitary, augmented isomorphism HHH H, where HH is the coalgebra belonging to G/G. (II) If the k-submodule of the fixelements of (HH)* is isomorphic to k (e.g. k principal or semilocal), then HH is a Frobeniusextension of the second kind. 相似文献
2.
Yūji Sakai 《Analysis Mathematica》1984,10(4):301-310
. (R)
–
–
fg(y)h(x–y) dx dy
–
–
f
^
(x)g
^
(y)h
^
(x–y)dx dy (f,g0) —:f×gf
^
×g
^(f,g 0) f^ g^ f g -, X — . , - f
1f
2 , f
1
^
×gf
2×g 0g. . 相似文献
3.
Selfadjoint linear pencils F–G are considered which have discrete spectrum and neither F nor G is definite. Several characterizations are given of a strongly definitizable property when F and G are bounded, and also when both operators are unbounded. The theory is applied to analysis of the stability of a linear second order initial-boundary value problem with boundary conditions dependent on the eigenvalue parameter.Research supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada. 相似文献
4.
On the x0y plane let there be specified a complete metric of negative curvature K by means of the line element ds2=dx2+B2(x, y) dy2, and, in the strip a={0xa, -4-bounded function B>0,K-2<0 ( and are constants). Then, the metric in strip a is embedded in R3 by means of a surface of class C3.Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 261–266, August, 1973. 相似文献
5.
6.
, . . .
The authors wish to thank the referee whose comments improved the presentation of the paper. In fact, the present form of Lemma 2, which was originally very long, is due to the referee. 相似文献
The authors wish to thank the referee whose comments improved the presentation of the paper. In fact, the present form of Lemma 2, which was originally very long, is due to the referee. 相似文献
7.
8.
H. Triebel 《Analysis Mathematica》1977,3(4):299-315
( « . III») - B
p,q
g(x)
F
p,q
g(x)
( ) R
n
. --, . : , , , . 相似文献
9.
10.
Ben Salem Nejib 《Journal of Theoretical Probability》1994,7(2):417-436
We consider hypergroups associated with Jacobi functions
()
(x), (–1/2). We prove the existence of a dual convolution structure on [0,+[i(]0,s
0]{{) =++1,s
0=min(,–+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem. 相似文献
11.
A. I. Il'inskii 《Mathematical Notes》1977,21(5):400-405
In the framework of the theory of D. Kendall's delphic semigroups are considered problems of divisibility in the semigroup of convex characteristic functions on the semiaxis (0,). Letn ()={:1¦11 or 1=}, and Io()={: 1¦ 1 N()}. The following results are proved: 1) The semigroup is almost delphic in the sense of R. Davidson. 2) N() is a set of the type G which is dense in (in the topology of uniform convergence on compacta). 3) The class Io() contains only the function identically equal to one.Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 717–725, May, 1977.The author thanks I. V. Ostrovskii for the formulation of the problem and valuable remarks. 相似文献
12.
Section 1 of the paper is devoted to extremal problems in the classes of conformal homeomorphisms of the circle and the annulus, connected directly with the problem on the maximum of the conformal modulus in the family of doubly connected domains. In Secs. 2 and 3 one considers the class R of functions f()=c1+c22+... regular and univalent in the circleU={||<1} and such that f(1)f(2)=1 for 12U (the class of Bieberbach-Eilenberg functions). Here one solves the problem of the maximum of |f(0)| in the class of functions f()R with a fixed value f(0, where 0 is an arbitrary point U, and of the maximum of |f(0)| in the entire class R. For the proof one makes use of the method of the moduli of families of curves.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 94–114, 1985. 相似文献
13.
K. Koncz 《Analysis Mathematica》1987,13(1):75-91
, (1). 3, , ()=, (8) (16). [1], . (28) (31) ( 5), - (. [3]).
The author thanks Professor M.Arató for having pointed out this problem, and for his valuable suggestions. 相似文献
The author thanks Professor M.Arató for having pointed out this problem, and for his valuable suggestions. 相似文献
14.
Tamotsu Tsuchikura 《Analysis Mathematica》1986,12(1):77-84
{n} a
n
n
, s
n
n- ,
n
-n- (, 1)- . . . -, . , «|s2n+1–s
2
n¦< . .» «¦
n
–
n–1¦< . .» .
s. , {a
n
} 0, a
n/n<, {a
n
} , {it|n¦<. , , -. 相似文献
15.
16.
Klaus Kalb 《manuscripta mathematica》1972,7(3):271-297
Let T be a selfadjoint operator in a Gelfand triplet H. Examples show that there can occur generalized eigenvalues of T which are not in the Hilbert space spectrum (T) of T. Moreover, the fuction d, which assigns to each real number s the dimension of the generalized eigenspace corresponding to s, can be essentially greater then the von Neumann multiplicity function of T. We therefore construct a new triplet H, closely related to the given Gelfand triplet, according to which the set of generalized eigenvalues of T is contained in (T), and the function d essentially equals the von Neumann multiplicity function of T. Then, in particular, the closure of the set of generalized eigenvalues equals (T). The expansion theorems in H are transferred to H.
Grundlage dieser Arbeit ist ein Teil meiner Dissertation. Ich danke Herrn Prof. Dr. H.G. Tillmann für die Anregung hierzu und für viele wertvolle Hinweise. 相似文献
Grundlage dieser Arbeit ist ein Teil meiner Dissertation. Ich danke Herrn Prof. Dr. H.G. Tillmann für die Anregung hierzu und für viele wertvolle Hinweise. 相似文献
17.
M. Rosenblatt 《Probability Theory and Related Fields》1966,6(4):293-301
Summary Consider a stationary process {X
n(), – < n < . If the measure of the process is finite (the measure of the whole sample space finite), it is well known that ergodicity of the process {X
n(), - < n < and of each of the subprocesses {X
n(), 0 n < , {X
n(), – < n 0 are equivalent (see [3]). We shall show that this is generally not true for stationary processes with a sigma-finite measure, specifically for stationary irreducible transient Markov chains. An example of a stationary irreducible transient Markov chain {X
n(), - < n <} with {itXn(), 0 n < < ergodic but {X
n(), < n 0 nonergodic is given. That this can be the case has already been implicitly indicated in the literature [4]. Another example of a stationary irreducible transient Markov chain with both {X
n(), 0 n < and {itX n(),-< < n 0} ergodic but {X
n(), - < n < nonergodic is presented. In fact, it is shown that all stationary irreducible transient Markov chains {X
n(), - < n < < are nonergodic.This research was supported in part by the Office of Naval Research.John Simon Guggenheim Memorial Fellow. 相似文献
18.
We obtain the analytic expression for the total cross section of the reaction e
–
e
+l
–
l
+ (l=,) taking possible quasianapole interaction effects into account. We find numerical restrictions on the interaction parameter value from data for the reaction e
–
e
+–+ in the energy domain below the Z
0 peak. 相似文献
19.
20.
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