Search Results - (Author, Cooperation:E. Palle)

2012-03-03

Nature Publishing Group (NPG)

0028-0836

1476-4687

Biology

Chemistry and Pharmacology

Medicine

Natural Sciences in General

Physics

Aerosols/analysis/chemistry ; Atmosphere/*chemistry ; *Earth (Planet) ; Extraterrestrial Environment/chemistry ; *Life ; Methane/analysis/metabolism ; Moon ; Oxygen/analysis/metabolism ; Ozone/chemistry ; Planets ; Plant Development ; Plants/metabolism/radiation effects ; Seawater/chemistry ; *Sunlight ; Time Factors

2018-06-02

MDPI Publishing

2073-8994

Mathematics

Physics

2018-12-21

American Association for the Advancement of Science (AAAS)

0036-8075

1095-9203

Biology

Chemistry and Pharmacology

Geosciences

Computer Science

Medicine

Natural Sciences in General

Physics

Astronomy, Geochemistry, Geophysics, Planetary Science

1089-7658

AIP Digital Archive

Mathematics

Physics

We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(∂/∂xj):j=1,...,d} with domain Cc∞(Ω) where the self-adjointness is defined relative to L2(Ω), and Ω is a given open subset of Rd. The measure on Ω is Lebesgue measure on Rd restricted to Ω. The problem originates with Segal and Fuglede, and is difficult in general. In this paper, we provide a representation-theoretic answer in the special case when Ω=I×Ω2 and I is an open interval. We then apply the results to the case when Ω is a d cube, Id, and we describe possible subsets Λ⊂Rd such that {eλ|Id:λ∈Λ} is an orthonormal basis in L2(Id). © 2000 American Institute of Physics.

Electronic Resource

1089-7658

AIP Digital Archive

Mathematics

Physics

We consider endomorphisms of von Neumann algebras: Let M be a von Neumann algebra, represented on a Hilbert space H, and let M′ be the corresponding commutant. Let α∈End(M) be given, and suppose M has a cyclic vector in H, such that the corresponding state leaves α invariant. Then there is a "dual'' completely positive mapping β on M′ which we find and describe: Each of the two α and β has an associated spectral group, and we show that the group for β is contained in that for α. We consider the following three restrictions on α: i) α is a shift on M, ii) α is strongly ergodic, and iii) α is ergodic. We give spectral theoretic conditions on α (using the two groups described above) to fall into each of the three classes. We also show that the two groups are conjugacy invariants, and we discuss the case of cocycle conjugacy. © 1996 American Institute of Physics.

Electronic Resource

1089-7658

AIP Digital Archive

Mathematics

Physics

In this paper we provide a quantitative comparison of two obstructions for a given symmetric operator S with dense domain in Hilbert space H to be self-adjoint. The first one is the pair of deficiency spaces of von Neumann, and the second one is of more recent vintage; Let P be a projection in H. We say that it is smooth relative to S if its range is contained in the domain of S. We say that smooth projections {Pi}i=1∞ diagonalize S if (a) (I−Pi)SPi=0 for all i, and (b) supi Pi=I. If such projections exist, then S has a self-adjoint closure (i.e., S¯ has a spectral resolution), and so our second obstruction to self-adjointness is defined from smooth projections Pi with (I−Pi)SPi≠0. We prove results both in the case of a single operator S and a system of operators. © 2000 American Institute of Physics.

Electronic Resource

1531-5851

42C05 ; 22D25 ; 46L55 ; 47C05 ; spectral pair ; translations ; tilings ; Fourier basis ; operator extensions ; induced representations ; spectral resolution ; Hilbert space

Springer Online Journal Archives 1860-2000

Mathematics

Abstract Let Ω ⊂ℝd have finite positive Lebesgue measure, and let $$\mathcal{L}^2$$ (Ω) be the corresponding Hilbert space of $$\mathcal{L}^2$$ -functions on Ω. We shall consider the exponential functionse λ on Ω given bye λ(x)=e i2πλ·x . If these functions form an orthogonal basis for $$\mathcal{L}^2$$ (Ω), when λ ranges over some subset Λ in ℝ d , then we say that (Ω, Λ) is a spectral pair, and that Λ is a spectrum. We conjecture that (Ω, Λ) is a spectral pair if and only if the translates of some set Ω′ by the vectors of Λ tile ℝd. In the special case of Ω=Id, the d-dimensional unit cube, we prove this conjecture, with Ω′=Id, for d≤3, describing all the tilings by Id, and for all d when Λ is a discrete periodic set. In an appendix we generalize the notion of spectral pair to measures on a locally compact abelian group and its dual.

Electronic Resource

1420-8989

Springer Online Journal Archives 1860-2000

Mathematics

Abstract Noncommutative differential geometric structures are considered for a class of simple C*-algebras. This structure is defined in terms of smooth Lie group actions on the C*-algebra in question together with a certain quantization mapping motivated directly by the known cohomological obstructions for the quantum mechanical quantization correspondence. We show that such a quantization mapping may be constructed for the C*-algebras associated to antisymmetric bi-characters and for the Cuntz/Cuntz-Krieger C*-algebras associated to topological dynamics. A certain curvature obstruction is defined in terms of the quantization mapping. It is shown that existence of smooth Lie group actions is determined by the curvature obstruction.

Electronic Resource

1420-8989

Primary 46L60 ; 47D25 ; 42A16 ; 43A65 ; Secondary 46L45 ; 42A65 ; 41A15

Springer Online Journal Archives 1860-2000

Mathematics

Abstract This paper is devoted to an approximation problem for operators in Hilbert space, that appears when one tries to study geometrically thecascade algorithm in wavelet theory. Let $$\mathcal{H}$$ be a Hilbert space, and let π be a representation ofL ∞( $$\mathbb{T}$$ ) on $$\mathcal{H}$$ . LetR be a positive operator inL ∞( $$\mathbb{T}$$ ) such thatR(1) =1, where1 denotes the constant function 1. We study operatorsM on $$\mathcal{H}$$ (bounded, but noncontractive) such that $$\pi (f){\rm M} = M\pi (f(z^2 ))andM*\pi (f)M = \pi (R*f),f \in L^\infty (\mathbb{T}),$$ where the * refers to Hilbert space adjoint. We give a complete orthogonal expansion of $$\mathcal{H}$$ which reduces π such thatM acts as a shift on one part, and the residual part is $$\mathcal{H}$$ (∞) = ∩ n [M n $$\mathcal{H}$$ ], where [M n $$\mathcal{H}$$ ] is the closure of the range ofM n . The shift part is present, we show, if and only if ker (M *)≠{0}. We apply the operator-theoretic results to the refinement operator (or cascade algorithm) from wavelet theory. Using the representation π, we show that, for this wavelet operatorM, the components in the decomposition are unitarily, and canonically, equivalent to spacesL 2(E n ) ⊂L 2(ℝ), whereE n ⊂ ℝ, n=1,2,3,..., ∞, are measurable subsets which form a tiling of ℝ; i.e., the union is ℝ up to zero measure, and pairwise intersections of differentE n 's have measure zero. We prove two results on the convergence of the cascale algorithm, and identify singular vectors for the starting point of the algorithm.

Electronic Resource

1432-1823

Springer Online Journal Archives 1860-2000

Mathematics

Electronic Resource

1432-1823

Springer Online Journal Archives 1860-2000

Mathematics

Electronic Resource

1432-1823

Springer Online Journal Archives 1860-2000

Mathematics

Electronic Resource

1420-8989

Primary 46L55 ; 47C15 ; Secondary 42C05 ; 22D25 ; 11B85

Springer Online Journal Archives 1860-2000

Mathematics

Abstract In this paper we show how wavelets originating from multiresolution analysis of scaleN give rise to certain representations of the Cuntz algebrasO N , and conversely how the wavelets can be recovered from these representations. The representations are given on the Hilbert space $$L^2 (\mathbb{T})$$ by (S i ξ) (z)=m i (z)ξ(z N ). We characterize the Wold decomposition of such operators. If the operators come from wavelets they are shifts, and this can be used to realize the representation on a certain Hardy space over $$L^2 (\mathbb{T})$$ . This is used to compare the usual scale-2 theory of wavelets with the scale-N theory. Also some other representations ofO N of the above form called diagonal representations are characterized and classified up to unitary equivalence by a homological invariant.

Electronic Resource

1432-2145

Pistacia vera ; Chalazogamy ; Ponticulus ; Pollen tube ; Ovule

Springer Online Journal Archives 1860-2000

Biology

Abstract The path of the pollen tube has been examined in pistachio (Pistacia vera), a chalazogamous species where the pollen tube penetrate the ovule via the chalaza. Special attention was paid to the way the pollen tube gains access to the ovule. A single anatropous ovule with a big funiculus occupies the entire ovary cavity. At anthesis, a physical gap exists between the ovule and the base of the style. However, upon pollen tube arrival a protuberance, the ponticulus, develops in the uppermost area of the funiculus between the style and ovule. This structure appears to facilitate access to the ovule by the pollen tube. The pollen tube penetrates the ovule via this ponticulus. Upon penetration, callose develops in the ponticulus cells surrounding the pollen tube. After pollen tube passage, the upper layer of the ponticulus lignifies and isolates the ovule from the style. This separation is further enlarged 2 weeks later when the ovary starts to develop without expansion of the ovule and a large gap develops separating the ovule from the style. Except for the induction of callose formation by the pollen tube in the funiculus, this process is independent of pollination and appears to be developmentally regulated since it occurs in the same way and at the same time in pollinated and unpollinated flowers. The ponticulus, although by a different mechanism, appears to be playing the role of an obturator regulating access of the pollen tube to the ovule. Furthermore, this access is restricted to a particular time during the development of the ovule.

Electronic Resource

1432-0916

Springer Online Journal Archives 1860-2000

Mathematics

Physics

Abstract Let τ be an action of a compact abelian groupG on aC*-algebraA, and assume that the fixed-point subalgebraA τ is an AF-algebra. We show that if δ is a closed *-derivation onA commuting with τ, and the restriction of δ toA τ generates a one-parameter group of *-automorphisms, then δ itself is a generator. In particular, the result applies if τ is an infinite product action ofG on a UHF algebra. Furthermore, if in this situation δ1 and δ2 are two derivations both satisfying the hypotheses on δ, and δ1 and δ2 have the same restriction toA τ, then there exists a one-parameter subgroup of the action τ with generator δ0 such thatD(δ1)∩D(δ2)∩D(δ0) is a joint core for the three derivations, and δ2=δ1+δ0 on this core.

Electronic Resource

1432-0916

Springer Online Journal Archives 1860-2000

Mathematics

Physics

Abstract The usual definition of approximately inner one-parameter groups of *-automorphisms ofC*-algebras (approximately inner dynamical one-parameter groups) contains a slight asymmetry. When this asymmetry is “corrected”, we show that if an approximately inner dynamical one-parameter group hasKMS states forone value of inverse temperature β=1/kT, then it hasKMS states for all values of β. By the Powers-Sakai Theorem it is enough to show that there is a trace state. We obtain a trace state as a limit of a sequence of “vector states” with respect to a givenKMS state and thus solve a problem raised in [6].

Electronic Resource

1432-2064

Springer Online Journal Archives 1860-2000

Mathematics

Summary Let $$\mathfrak{A}$$ denote the extended Weyl algebra, $$\mathfrak{A}_0 \subset \mathfrak{A}$$ , the Weyl algebra. It is well known that every element of $$\mathfrak{A}$$ of the formA=ΣB k * B k is positive. We prove that the converse implication also holds: Every positive elementA in $$\mathfrak{A}$$ has a quadratic sum factorization for some finite set of elements (B k ) in $$\mathfrak{A}$$ . The corresponding result is not true for the subalgebra $$\mathfrak{A}_0 $$ . We identify states on $$\mathfrak{A}_0 $$ which do not extend to states on $$\mathfrak{A}$$ . It follows from a result of Powers (and Arveson) that such states on $$\mathfrak{A}_0 $$ cannot be completely positive. Our theorem is based on a certain regularity property for the representations which are generated by states on $$\mathfrak{A}$$ , and this property is not in general shared by representations generated by states defined only on the subalgebra $$\mathfrak{A}_0 $$ .

Electronic Resource

1432-1807

Springer Online Journal Archives 1860-2000

Mathematics

Electronic Resource

1432-1807

Springer Online Journal Archives 1860-2000

Mathematics

Electronic Resource

1432-1807

Springer Online Journal Archives 1860-2000

Mathematics

Electronic Resource