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1.
Canonical representations on Hermitian symmetric spaces G/K were introduced by Vershik, Gelfand and Graev and Berezin. They are unitary. We study canonical representations in a wider sense. In this paper we restrict ourselves to a crucial example – the Lobachevsky plane: G=SU(1,1), K=U(1). Canonical representations are labelled by the complex parameter (Vershik–Gelfand–Graev's representations correspond to –3/2<<0). We decompose the canonical representations into irreducible components. The decomposition includes boundary representations generated by the canonical representations. So we study these boundary representations themselves. The decomposition of boundary representations is closely connected with the meromorphic structure of Poisson and Fourier transforms associated with canonical representations. In particular, second-order poles give second-order Jordan blocks. Finally, we give a full decomposition of the Berezin transform using generalized powers (Pochhammer symbols) instead of usual powers of . 相似文献
2.
Given a bounded linear operatorA in an infinite dimensional Banach space and a compact subset of a connected component of its semi-Fredholm domain, we construct a finite rank operatorF such that –A+F is bounded below (or surjective) for each ,F
2=0 and rankF=max min{dimN(–A), codimR(–A)}, if ind(–A)0 (or ind(–A)0, respectively) for each . 相似文献
3.
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
4.
Robert Roussarie 《Bulletin of the Brazilian Mathematical Society》1998,29(2):229-251
LetH be a germ of holomorphic diffeomorphism at 0 . Using the existence theorem for quasi-conformal mappings, it is possible to prove that there exists a multivalued germS at 0, such thatS(ze
2i
)=HS(z) (1). IfH
is an unfolding of diffeomorphisms depending on (,0), withH
0=Id, one introduces its ideal
. It is the ideal generated by the germs of coefficients (a
i
(), 0) at 0
k
, whereH
(z)–z=a
i
()z
i
. Then one can find a parameter solutionS
(z) of (1) which has at each pointz
0 belonging to the domain of definition ofS
0, an expansion in seriesS
(z)=z+b
i
()(z–z
0)
i
with
, for alli.This result may be applied to the bifurcation theory of vector fields of the plane. LetX
be an unfolding of analytic vector fields at 0 2 such that this point is a hyperbolic saddle point for each . LetH
(z) be the holonomy map ofX
at the saddle point and
its associated ideal of coefficients. A consequence of the above result is that one can find analytic intervals , , transversal to the separatrices of the saddle point, such that the difference between the transition mapD
(z) and the identity is divisible in the ideal
. Finally, suppose thatX
is an unfolding of a saddle connection for a vector fieldX
0, with a return map equal to identity. It follows from the above result that the Bautin ideal of the unfolding, defined as the ideal of coefficients of the difference between the return map and the identity at any regular pointz, can also be computed at the singular pointz=0. From this last observation it follows easily that the cyclicity of the unfoldingX
, is finite and can be computed explicity in terms of the Bautin ideal.Dedicated to the memory of R. Mañé 相似文献
5.
Reverse Functional Inequalities and Their Applications to Nonlinear Elliptic Boundary Value Problems
We establish some reverse inequalities. We give applications to nonlinear elliptic boundary value problems containing a parameter which have two branches of solutions u
(0) and U
(>0) of which the first is continuous at the origin and the second increases indefinitely as 0. 相似文献
6.
Résumé Soit (V
)0 une résolvante définie sur un espace mesurable telle que le noyau initial est borné; on trouve une condition nécéssaire et suffisante pour qu'un noyau borné U possède une résolvante (U
)0 telle que U
V
pour tout 0. On donne plusieurs applications de ce résultat. 相似文献
7.
C. Berg 《Aequationes Mathematicae》1990,40(1):83-88
Summary The integral
-
[C
2n
(it)]–2(1+t
2)–-1/2
dt is evaluated for > –1/2 whereC
2n
is the Gegenbauer polynomial of degree 2n. Letting gives the value
-
[H
2n
(it)]–2
e
1-1/2t
2
dt involving the Hermite polynomialH
2n
of degree 2n. The result is obtained using Gegenbauer functions of the second kind. 相似文献
8.
Nikolaos S. Papageorgiou 《Analysis Mathematica》1991,17(2):141-152
9.
G. V. Radzievskii 《Ukrainian Mathematical Journal》1994,46(5):581-603
We study the minimality of elementsx
h,j,k
of canonical systems of root vectors. These systems correspond to the characteristic numbers
k
of operator functionsL() analytic in an angle; we assume that operators act in a Hilbert space
. In particular, we consider the case whereL()=I+T()c, >0,I is an identity operator,C is a completely continuous operator, (I- C)–1c for ¦arg¦, 0<<, the operator functionT() is analytic, and T()c for ¦arg¦<. It is proved that, in this case, there exists >0 such that the system of vectorsC
v
x
h,j,k
is minimal in
for arbitrary positive <1+, provided that ¦k¦>.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 545–566, May, 1994.This research was partially supported by the Ukrainian State Committee of Science and Technology. 相似文献
10.
Letf=f
+f
–f
f
0 be a linear direct sum decomposition of a real endomorphismf End
n
, where the components correspond respectively to absolute values of eigenvalues ||: 0<||<1(f
+); ||>1(f
–); ||=0(f
); and ||=1(f
0). We conjecture that a complete set of invariants with respect to topological equivalence consists of the dimensions and orientations off
+ and off
–, together with the linear isomorphy classes off
andf
0. We prove that this is true in case
n
contains nof-periodic points of periods 5 or 7. The conjecture is also true in case it is true for all periodic rotations. In §9 we make some comments on this unsolved case. The main interest of the paper is in §6 and 7.Research supported by the National Science Foundation (Contract number 144-B 695), the Wisconsin Alumni Research Foundation (project number 120432), and l'Institut des Hautes Etudes Scientifiques. 相似文献
11.
Let G=A
ut(T) be the group of automorphisms of a homogeneous tree and let d(v,gv) denote the natural tree distance. Fix a base vertex e in T. The function (g)=exp(–d(e,ge)), being positive definte on G, gives rise to a semigroup of states on G whose infinitesimal generator d/d|=0=log() is conditionally positive definite but not positive definite. Hence, log() corresponds to a nontrivial cocycle (g): GH
in some representation space H
. In contrast with the case of PGL(2,), the representation is not irreducible.Let
o
(g) be the derivative of the spherical function corresponding to the complementary series of A
ut(T). We show that –d(e,ge) and
o
(g) come from cohomologous cocycles. Moreover,
o
is associated to one of the two (irreducible) special representations of A
ut(T). 相似文献
12.
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
13.
V. M. Petrichkovich 《Journal of Mathematical Sciences》1999,96(2):3022-3025
We describe all the factorizations A=BC (up to associates) of a matrix A over a commutative principal ideal domain parallel to the factorization DA= of its canonical diagonal form DA ( and are diagonal matrices), that is, the factorizations such that the matrices B and C are equivalent to the matrices and respectively.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 96–100. 相似文献
14.
A stochastic model of an epidemic is investigated, taking account of the removal of ill members of the population (by death, by recovery with immunization, by isolation) and natural immunization. Limiting distributions are found for the size of the epidemic, the number immunized
1, and their sum, under the assumption that the original number of susceptible individuals n and the number of ill individuals m , while n 1,n
0< , where and are the coefficients for the contraction of the disease and of immunization respectively.Translated from Matematicheskie Zametki, Vol. 8, No. 3, pp. 385–392, September, 1970. 相似文献
15.
V. I. Ladygin 《Mathematical Notes》1978,23(1):51-58
A condition is obtained on the placement of point n (in some sense, the final point) with which completeness of the system of functionsexp (–
n
x), Ren>0, in spaces Lp, 1p<2. is equivalent to divergence of the series ren(1+¦n¦2)–1.Translated from Matematicheskie Zametki, Vol. 23, No. 1, pp. 91–103, January, 1978.Deceased. 相似文献
16.
A. V. Bakhshetsyan 《Analysis Mathematica》1988,14(2):157-174
{
d
} , c
n
n
(x) , {c
n
}l
2. () . , .. 1) ()< { n} — , {(n)} m .2) ()=, {n {cn}l
2 , c
n
(n) . , {
n
} . 相似文献
17.
Michael Sand 《Integral Equations and Operator Theory》1996,26(2):210-221
If is a complex, separable Hilbert space, letL
2 () denote theL
2-space of functions defined on the unit circle and having values in . The bilateral shift onL
2() is the operator (U
f)()=f(). A Hilbert spaceH iscontractively contained in the Hilbert spaceK ifHK and the inclusion mapH–K is a contraction. We describe the structure of those Hilbert spaces, contractively contained inL
2(), that are carried into themselves contractively byU
. We also do this for the subcase of those spaces which are carried into themselves unitarily byU
. 相似文献
18.
Akos Seress 《Designs, Codes and Cryptography》2001,22(1):5-17
A-design is a family B
1,B
2,...,B
v
of subsets of X={1, 2,..., v} such that B
i
B
j
= for all i jand not all B
i
are of the same size. Ryser's andWoodall's -design conjecture states thateach -design can be obtained from a symmetricblock design by a certain complementation procedure. Our mainresult is that the conjecture is true when is twice a prime number. 相似文献
19.
P. E. Markov 《Journal of Mathematical Sciences》1994,72(4):3191-3200
For a Cr,-immersion z:X E, r 2, 0 < < 1, of an n-dimensional (n 1) simply-connected Cr+2,-manifold X into Euclidean space E, the metric I(z) induced by z has a neighborhood in Cr,-topology in which every metric from a given subbundle of metrics is Cr,-immersible into E. In particular, it is proved that metric ds
0
2
of the Riemannian product of p spheres of dimensions 1, , p 2 has a neighborhood in C2,-topology from which any conformally equivalent metric to ds
0
2
, is immersible into E with dimE = 1 + +
p
+ p. The proofs are based on the investigation of a varied system of Gauss—Codazzi—Ricci equations for an infinitely small deformation of surface z(X) in E with a prescribed variation of the metric.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 49–67, 1992. 相似文献
20.
J. Płonka 《Acta Appl Math》1998,52(1-3):305-313
Let : F N be a type of algebras, where F is a set of fundamental operation symbols and N is the set of nonnegative integers. An identity of type is called biregular if the sets of variables in and are identical and the sets of fundamental operation symbols in and are identical. If K is a variety of type , we denote by Kb the variety of type defined by all biregular identities from Id(K). Kb will be called the biregularization of K. In this paper we give a representation of free algebras over Kb by means of free algebras over K. 相似文献