共查询到20条相似文献,搜索用时 15 毫秒
1.
V. F. Molchanov 《Journal of Mathematical Sciences》2007,141(4):1432-1451
The two-sheeted hyperboloid
in ℝn can be identified with the unit sphere Ω in ℝn with the equator removed. Canonical representations of the group G = SO
0(n − 1, 1) on
are defined as the restrictions to G of the representations of the overgroup
= SO
0(n, 1) associated with a cone. They act on functions and distributions on the sphere Ω. We decompose these canonical representations
into irreducible constituents and decompose the Berezin form. Bibliography: 12 titles.
To the memory of my teacher F. A. Berezin
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 331, 2006, pp. 91–124. 相似文献
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U. M. Pachev 《Journal of Mathematical Sciences》1982,19(2):1122-1155
Yu. V. Linnik's investigations [Vestn. Leningr. Univ., No. 2, 3–23; No. 5, 3–32; No. 8, 15–27 (1955)] are refined and generalized to indefinite ternary quadratic forms of a sufficiently general form (to forms contained in the form x1x3—x
2
2
]. The method of investigation is improved. The presentation is substantially simplified.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 93, pp. 87–141, 1980. 相似文献
6.
We consider measurable subsets {ofR}n with 0<m()<, and we assume that has a spectral set . (In the special case when is also assumed open, may be obtained as the joint spectrum of a family of commuting self-adjoint operators {H
k: 1kn} in L
2 () such that each H
k is an extension of i(/x
k) on C
c
(), k=1, ..., n.)It is known that is a fundamental domain for a lattice if is itself a lattice. In this paper, we consider a class of examples where is not assumed to be a lattice. Instead is assumed to have a certain inhomogeneous form, and we prove a necessary and sufficient condition for to be a fundamental domain for some lattice in {ofR}n. We are thus able to decide the question, fundamental domain or not, by considering only properties of the spectrum . Our criterion is obtained as a corollary to a theorem concerning partitions of sets which have a spectrum of inhomogeneous form.Work supported in part by the NSF.Work supported in part by the NSRC, Denmark. 相似文献
7.
Abstract. We construct determinantal expressions for the zonal spherical functions on the hyperboloids with p,q odd (and larger than 1). This gives rise to explicit evaluation formulas for hypergeometric series representing half-integer
parameter families of Jacobi functions and (via specialization) Jacobi polynomials.
Received November 18, 1999 / Published online October 30, 2000 相似文献
8.
Alan L.T Paterson 《Journal of Functional Analysis》1983,53(3):203-223
A theory of harmonic analysis on a metric group (G, d) is developed with the model of U, the unitary group of a C1-algebra , in mind. Essential in this development is the set of contractive, irreducible representations of G, and its concomitant set Pd(G) of positive-definite functions. It is shown that is compact and closed in . The set is determined in a number of cases, in particular when G = U() with abelian. If is an AW1-algebra, it is shown that d is essentially the same as . Unitary groups are characterised in terms of a certain Lie algebra u and several characterisations of G = U() when is abelian are given. 相似文献
9.
If we change the sign of p ? m columns (or rows) of an m × m positive definite symmetric matrix A, the resultant matrix B has p negative eigenvalues. We give systems of inequalities for the eigenvalues of B and of the matrix obtained from B by deleting one row and column. To obtain these, we first develop characterizations of the eigenvalues of B which are analogous to the minimum-maximum properties of the eigenvalues of a symmetric A, i.e. the Courant-Fischer theorem. These results arose from studying probability distributions on the hyperboloid of revolution . By contrast, the familiar results are associated with the sphere x21 + ? + x2m = 1. 相似文献
10.
Results of B. F. Skubenko (Izv. Akad. Nauk SSSR, Ser. Mat.,26, 721–752 (1962)) are generalized to indefinite ternary quadratic formsf(x)=f
0(Cx), which are contained in the simplest formf
0(x)=x
1
x
3–x
r
e
We prove that the integral points on the hyperboloid of one sheetf(x)=m,m<0,
are uniformly distributed over area (in the sense of hyperbolic metric) and over residue classes for given modulus.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 121, pp. 83–93, 1983. 相似文献
11.
Moscow State University. L'vov Polytechnical Institute. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 24, No. 1, pp. 69–71, January–March, 1990. 相似文献
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We study some spectral properties of the adjacency operator of non-homogeneous networks. The graphs under investigation are obtained by adding density zero perturbations to the homogeneous Cayley Trees. Apart from the natural mathematical meaning, such spectral properties are relevant for the Bose Einstein Condensation for the pure hopping model describing arrays of Josephson junctions on non-homogeneous networks. The resulting topological model is described by a one particle Hamiltonian which is, up to an additive constant, the opposite of the adjacency operator on the graph. It is known that the Bose Einstein condensation already occurs for unperturbed homogeneous Cayley Trees. However, the particles condensate on the perturbed graph, even in the configuration space due to non-homogeneity. Even if the graphs under consideration are exponentially growing, we show that it is enough to perturb in a negligible way the original graph in order to obtain a new network whose mathematical and physical properties dramatically change. Among the results proved in the present paper, we mention the following ones. The appearance of the Hidden Spectrum near the zero of the Hamiltonian, or equivalently below the norm of the adjacency. The latter is related to the value of the critical density and then with the appearance of the condensation phenomena. The investigation of the recurrence/transience character of the adjacency, which is connected to the possibility to construct locally normal states exhibiting the Bose Einstein condensation. Finally, the study of the volume growth of the wave function of the ground state of the Hamiltonian, which is nothing but the generalized Perron Frobenius eigenvector of the adjacency. This Perron Frobenius weight describes the spatial distribution of the condensate and its shape is connected with the possibility to construct locally normal states exhibiting the Bose Einstein condensation at a fixed density greater than the critical one. 相似文献
14.
The method of approximative inverse operators is applied to the inversion of certain potential-type operators with symbols degenerate on hyperboloids or paraboloids. Using this method, the inversion is constructed as the limit of a sequence of convolutions with summable kernels that are expressed in terms of elementary or special functions. 相似文献
15.
J.-F. Quint 《Journal of Functional Analysis》2009,256(10):3409-3460
In this paper, we completely determine the spectral invariants of an auto-similar planar 3-regular graph. Using the same methods, we study the spectral invariants of a natural compactification of this graph. 相似文献
16.
Ronald L. Lipsman 《Israel Journal of Mathematics》1986,54(3):335-350
It is proven that theL
2 spectrum for certain non-semisimple, non-nilpotent symmetric spaces is multiplicity-free. The spectrum and spectral measure
are computed precisely for symmetric spaces corresponding to non-compact motion groups. Somewhat less complete results on
theL
2 spectrum — in both the Mackey Machine and Orbit Method modes — are given for general semidirect product symmetric spaces.
The author was supported by the NSF through DMS84-00900-A01 and by a Senior Fulbright Fellowship. 相似文献
17.
M. Laczkovich G. Szé kelyhidi 《Proceedings of the American Mathematical Society》2005,133(6):1581-1586
Let be an Abelian group and let denote the linear space of all complex-valued functions defined on equipped with the product topology. We prove that the following are equivalent.
(i) Every nonzero translation invariant closed subspace of contains an exponential; that is, a nonzero multiplicative function.
(ii) The torsion free rank of is less than the continuum.
18.
A. A. Osinenko 《Journal of Mathematical Sciences》2012,181(6):886-913
The goal of harmonic analysis on the infinite-dimensional unitary group is to decompose a certain family of unitary representations of this group, which is a substitute for the nonexisting regular representations and depends on two complex parameters (Olshanski, 2003). In the case of noninteger parameters, the decomposing measure is described in terms of determinantal point processes (Borondin and Olshanski, 2005). The aim of the present paper is to describe the decomposition for integer parameters; in this case, the spectrum of the decompositions changes drastically. A similar result was earlier obtained for the infinite symmetric group (Kerov, Olshanski, and Vershik, 2004), but the case of the unitary group turned out to be much more complicated. In the proof we use Gustafson’s multilateral summation formula for hypergeometric series. Bibliography: 6 titles. 相似文献
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