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Volume 33 (1997)
- Issue 6 Pages 869-
- Issue 5 Pages 713-
- Issue 4 Pages 509-
- Issue 3 Pages 331-
- Issue 2 Pages 189-
- Issue 1 Pages 1-
Volume 33, Issue 6
Displaying 1-6 of 6 articles from this issue
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Reinhard Honegger, Alfred Rieckers1997 Volume 33 Issue 6 Pages 869-892
Published: 1997
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSSqueezing processes are commonly described in terms of quadratic Hamiltonians, which generate unitary implementations of Bogoliubov transformations of the quantized electromagnetic field. Here the behaviour of the quasifree, the classical, and the coherent photon states under general squeezing Bogoliubov transformations is investigated. It is found that there is a great variety of mixed classical states, which remain classical under the squeezing operation, whereas each pure classical state becomes non-classical. Especially, some classical, microscopic first order coherent states remain classical and coherent of first order under one-mode squeezing. This contrasts squeezing of macroscopic coherent states.View full abstractDownload PDF (2685K) -
Christophe Mourougane1997 Volume 33 Issue 6 Pages 893-916
Published: 1997
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSOur main purpose is to study ampleness and positivity properties of the direct image φ{\bigstar}L of a holomorphic line bundle L under a smooth morphism φ: X→Y between compact complex analytic manifolds. We show that in general the ampleness of L does not imply that of the direct image φ{\bigstar}L but only that of the direct image of the adjoint line bundle φ{\bigstar}(KX/Y⊗L).View full abstractDownload PDF (2246K) -
Tiberiu Constantinescu, Aurelian Gheondea1997 Volume 33 Issue 6 Pages 917-951
Published: 1997
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSHermitian kernels are studied as generalizations of kernels of positive type. The main tool is the axiomatic concept of induced Krein space. The existence of Kolmogorov decompositions of a hermitian kernel and their uniqueness, modulo unitary equivalence, are characterized. The existence of reproducing kernel Krein spaces is shown to be equivalent to the existence of Kolmogorov decompositions. Applications Applications to the Naimark dilations of Toeplitz hermitian kernels on the set of integers and to the uniqueness of the Krein space completions of nondegenerate inner product spaces are included.View full abstractDownload PDF (3891K) -
Yutaka Saburi1997 Volume 33 Issue 6 Pages 953-966
Published: 1997
Released on J-STAGE: January 22, 2009
JOURNAL FREE ACCESSThe characterization of Fourier series of real analytic functions and hyperfunctions on compact Lie groups is discussed by means of complex analysis.View full abstractDownload PDF (1474K) -
Hiroaki Shimomura1997 Volume 33 Issue 6 Pages 967-985
Published: 1997
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSLet H be a separable Hilbert space over R (dim (H) is finite or infinite), Ha be the algebraic dual space of H, \mathfrak{B} be the cylindrical σ-algebra on Ha and μ be a rotationally invariant probability measure on (Ha, \mathfrak{B}). Further let θ=θ(x, U) be a 1-cocycle defined on (x, U)∈Ha×O(H), where O(H) is the rotation group on H. That is,
(c.1) for any fixed U∈O(H), θ(x, U) is a \mathfrak{B}-measurable function of x,
(c.2) | θ(x, U) |≡1, and
(c.3) for ∀U1, ∀U2∈O(H), θ(x, U1)θ(tU1x, U2)=θ(x, U1U2) for μ-a.e.x,
where tU is the algebraic transpose of U. Moreover it is said to be continuous, if the following condition holds for θ.
(c.4) θ(x, U)→1 in μ, if U→Id in the strong operator topology.
Our main result is as follows.
Assume that dim (H)≠3. Then for any continuous 1-cocycle θ, there exists a \mathfrak{B}-measurable function φ with modulus 1 such that for any fixed U∈O(H), θ(x, U)=φ(tUx)/φ(x) for μ-a.e.x.View full abstractDownload PDF (1564K) -
Atsushi Nakayashiki1997 Volume 33 Issue 6 Pages 987-1015
Published: 1997
Released on J-STAGE: April 24, 2009
JOURNAL FREE ACCESSWe shall give an elementary and rigorous proof of the Thomae formula for ZN curves which was discovered by Bershadsky and Radul [1, 2]. Instead of using the determinant of the Laplacian we use the traditional variational method which goes back to Riemann, Thomae, Fuchs. In the proof we made explicit the algebraic expression of the chiral Szegö kernels and prove the vanishing of zero values of derivatives of theta functions with ZN invariant 1/2N characteristics.View full abstractDownload PDF (2058K)
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